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∫ x radical (2x-x ^ 2) DX
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∫ x radical (2x-x ^ 2) DX = ∫ x radical (- 1 + 2x-x ^ 2 + 1) DX = ∫ x radical (1 - (x-1) ^ 2DX)
Let t = X-1
=∫ (T + 1) root sign (1-T ^ 2) DT, then integral by parts
∫ x√(2x - x²) dx
= ∫x√[- (x² - 2x + 1) + 1] dx
= ∫x√[1 - (x - 1)²] dx
Let X - 1 = sin θ, DX = cos θ D θ
= ∫(1 + sinθ)|cosθ| * cosθ dθ
= ∫(1 + sinθ)cos²θ dθ
=... unfold
∫ x√(2x - x²) dx
= ∫x√[- (x² - 2x + 1) + 1] dx
= ∫x√[1 - (x - 1)²] dx
Let X - 1 = sin θ, DX = cos θ D θ
= ∫(1 + sinθ)|cosθ| * cosθ dθ
= ∫(1 + sinθ)cos²θ dθ
= ∫cos²θ dθ + ∫(- π/2，π/2) sinθcos²θ dθ
=∫cos2 + ∫ (θ s) / 2
Is the recommended answer right. Part two?? Do a good calculation,
As shown in the figure, ABC is known to be three points on the number axis, and point C corresponds to the number
As shown in the figure, given that points a, B and C are three points on the number axis, the corresponding number of point C is 6, BC = 4 and ab = 12. (1) find the corresponding number of a and B
(2) The moving points P and Q start from a and C at the same time and move along the positive direction of the number axis at the speed of six units and three units per second, respectively. M is the midpoint of AP, n is on CQ, and CN = one third of CQ. Let time be t (t > 0)
To find the number corresponding to Mn (expressed by the algebraic formula containing T)
B is 2, a is - 10
M is 3t-5 and N is t + 2
Given that the function f (x) = x ^ 2 + 2 (A-1) x + 2 is a decreasing function in the interval (negative infinity, 4), find the value range of real number a,
For the quadratic function f (x) = x ^ 2 + 2 (A-1) x + 2, the opening is upward,
Axis of symmetry x = - 2 (A-1) / 2 = 1-A,
Monotonically decreasing on (- ∞, 1-A), monotonically increasing on [1-A, + ∞)
There are 4 ≤ 1-A a ≤ - 3
In the international system of units, what is the unit of speed? What is the symbol?
Thank you!
It's meters per second, M / s
Primary school sixth grade mathematics addition, subtraction, multiplication and division mixed operation 70, kneeling, emergency
1.3/7 × 49/9 - 4/3 2.8/9 × 15/36 + 1/27 3.12× 5/6 – 2/9 ×3 4.8× 5/4 + 1/4 5.6÷ 3/8 – 3/8 ÷6 6.4/7 × 5/9 + 3/7 × 5/9 7.5/2 -（ 3/2 + 4/5 ） 8.7/8 + （ 1/8 + 1/9 ） 9.9 × 5/6 + 5/6 10.3/4 ×...
If the function f (x) = x2 + 2 (A-1) x + 2 is a decreasing function on (- ∞, 4], then the value range of real number a is ()
A. a≤-3B. a≥-3C. a≤5D. a≥5
∵ f (x) = x2 + 2 (A-1) x + 2 = (x + A-1) 2 + 2 - (A-1) 2, its axis of symmetry is: x = 1-A ∵ function f (x) = x2 + 2 (A-1) x + 2 is a decreasing function on (- ∞, 4], so a is selected
For example, for a consumer in a circuit, when the resistance of the consumer increases, the electric power increases or decreases. Which formula should be used
The teacher talked about two formulas of electric power, one is the ratio of u to R, and the other is the ratio of I to R. if the resistance becomes larger, the former means that the electric power becomes smaller, and the latter means that the electric power becomes larger. When to use which formula? This problem has puzzled me for a long time
It depends on whether the voltage at both ends of the appliance changes,
For example, parallel circuit: voltage unchanged, use p = U2 / R, resistance larger, power smaller
If you use p = I2R, it must be considered that the increase of resistance will cause the current of the branch to decrease
The key of electricity is to choose the right formula according to the specific situation of the topic, sum up carefully, and master it. Come on!
Addition, subtraction, multiplication and division of quadratic radical
There are some ways to learn the second radical. If you practice frequently, you can master it well
Addition and subtraction: they can be classified into the same category. Those with the same number under the root sign can be operated, otherwise they cannot be added or subtracted
Multiplication and division: when multiplying, remember the same two root sign items, that is, the numbers under the root sign are the same, multiply to remove the root sign; division becomes one, and finally rationalize the denominator
The most worthy problem is similar to the problem of double root sign 5 plus 6 root. At this time, we should imitate the square form of root sign a plus root sign B
The root sign term is changed into 2 times the root sign AB, and the integer term is changed into a plus B. for example, 2 times the root sign 5 is 2 times the root sign 1 times the root sign 5, and 6 is 1 plus 5, so the original formula after square root is root sign 5 plus 1, and so on
May you make progress and ask again
Let f (x) = root ax & sup2; + BX + C (a < 0) be defined as d if all points (s, f (T)) (s, t ∈ d) form a square
I want to ask why (B & # 178; - 4ac) / 4A needs a root
Sorry, wrong question. (4ac-b & # 178;) / 4A why root
Let's find the root by △ method. The △ itself is in the root sign
What is the formula for calculating the electric power of electric appliance with non pure resistance
It's UI. That's right
For example, the motor is not pure resistance
What is his total power
But the thermal power is the square of I, R
The two are not equal
It shows that Ohm's law is not applicable in non pure resistance circuit
But p is UI
p=ui
P = I * u * cosa, where cosa is the power factor and a is the phase difference between current and voltage.
UI is not wrong, UI is the most primitive formula, there will be no mistake
RELATED INFORMATIONS
- 1. Given that points a, B and C are three points on the number axis, the number corresponding to point C is 6, BC = 4, ab = 12. (1) find the number corresponding to points a and B. (2) the moving points P and Q start from a and C at the same time. They move along the positive direction of the number axis at the speed of 6 units per second and 3 units per second, respectively. M is the midpoint of a and P, n is on C and Q, and CN = one third CQ. Let t (T > 0) be the moving time, When the number corresponding to n (expressed by the formula containing T) is the value of T, OM = 2bn
- 2. As shown in the figure, it is known that A.B.C is three points on the number axis, and the number represented by point C is 6, BC = 4, ab = 12 The moving point P.Q starts from A.C. at the same time, the point P-2 unit length per second has a uniform speed of work along the number axis, and the point Q-1 unit length per second has a uniform speed of work along the number axis to the left. Suppose the movement time is t (T > 0), and what is the value of T, one of the three points o and P.Q is exactly the midpoint of the line segment connected by the other two points
- 3. As shown in the figure, point C is on the number axis, and AC: BC = 1:5, find the number corresponding to point C. 2) if a starts from a and B at the same time, the speed of a is 3 times slower than that of A Bit / s, meet 2 units from the origin, the equation graph is a straight line, a is - 10, B is 14
- 4. On the number axis, O is the origin, a and B are - 8 and 2, respectively 1. Finding the length of ab 2. The moving point P starts from a and moves to the right along the number axis with a speed of 3 unit lengths per second; meanwhile, the moving point Q starts from B and moves to the left along the number axis with a speed of 1 unit length per second. When P and Q coincide, the two points stop moving at the same time. Let the movement time of the two points be T seconds, and a formula containing t be used to express the length of the segment PQ 3. Under the condition of (2), the distance from point P and Q to origin o is equal when t is the value And do timely explanation, the more detailed the better, 3Q~
- 5. On the number axis, points a and B represent rational numbers a and B respectively, and the origin o is just the midpoint of AB, then the value of (a + b) 100 + (A / b) 2008 is (a + b) 100 (A / b) 2008
- 6. On the number axis, the distance from point a to the origin is 3, and the distance from point B to the origin is 4
- 7. A point on the number axis that represents an integer is called an integral point. The unit length of a certain number axis is 1 cm. If you draw a line AB with the length of 2008 cm randomly on the number axis
- 8. On the number axis, point a stands for negative 6, and point B stands for positive 4. Please divide line AB into five equal parts, and the point is cdef from left to right. Write down the numbers they represent
- 9. The moving point a starts from the origin and moves along the negative direction of the number axis, while the moving point C on the number axis always moves along the number axis at a speed of 10 unit length / s Moving point a starts from the origin and moves in the negative direction along the number axis, while moving point B also starts from the origin and moves in the positive direction along the number axis. After 4 seconds, the two points are 20 unit lengths apart. It is known that the velocity ratio of moving point a and B is 2:3 (1). Calculate the velocity of two moving points (2). If two points a and B start from the positions marked in (1) at the same time, they move in the negative direction along the number axis according to the original velocity, A few seconds later, the origin is just in the middle of the two moving points (3) on the number axis, and the moving point C has been moving along the number axis at a speed of 10 unit length / second. When a and B start from the position marked in (1) and move in the negative direction of the number axis, the moving point will catch up with a and then return to B, and then reverse a when B meets. In this way, when B catches up with a, C stops moving immediately, How many unit lengths does point C move
- 10. The number corresponding to point a on the number axis is - 5. Point B is on the right side of point A. electronic ant a and B move to the left at the speed of 2 units / s and 1 unit / s respectively in B. electronic ant a and B move to the left at the speed of 1 unit / s Ant C moves to the right at a speed of 3 units per second Let the time of their simultaneous departure be T seconds. Is there a value of t so that the distance between C and B is twice that between C and a? If there is a value of T, please explain the reason
- 11. "24" point game, with 2, 6, 9, 9 together into 24 points (each number only once), the formula is______ .
- 12. (1) 2, - 4,8,11 use these four numbers to do a 24 point game (2) and the other four numbers 3, - 7,8,13 can be made equal to 24 by ()
- 13. 7 6 2 8 9 1 6 2 is 24 points Space in the middle
- 14. My mother loves singing very much
- 15. A very interesting playground
- 16. Her mother walks to work every day
- 17. Xiaohong, Xiaohua and Xiaoli go to the bookstore together to buy the same book. If each person buys one book, Xiaohong's difference is 2.4 yuan, Xiaohua's difference is 4.5 yuan, and Xiaoli's difference is 0.5 yuan; If the sum of three people's money is just enough to buy two books, then one book is () yuan, and Xiao Li brings () yuan more than Xiao Hong?
- 18. One day, Xiaohong and Xiaoli used the temperature difference to measure the height of the mountain. Xiaohong measured the temperature at the top of the mountain to be - 4 ℃, and Xiaoli measured the temperature at the foot of the mountain to be 6 ℃. It is known that every 100 meters increase in the height of the area, the temperature will decrease by about 0.8 ℃, and the height of the mountain is about 10 ℃______ Rice
- 19. The ratio of extracurricular books between Xiaohong and Xiaoli is 2:1. If Xiaohong lends 11 books to Xiaoli, the ratio of extracurricular books between Xiaohong and Xiaoli is 7:20 How many extra-curricular books did Xiao Hong and Xiao Li have?
- 20. Xiao Li's family will travel from Xi'an to Harbin, while Xiao Hua's family will go on holiday from Harbin to Xi'an Xiaoli's family will travel from Xi'an to Harbin, and Xiaohua's family will take a vacation from Harbin to Xi'an. The railway from Xi'an to Harbin is about 2600 kilometers long. At 8 a.m. on New Year's day, Xiaoli's family will start from Xi'an by train, which runs 60 kilometers per hour. At the same time, Xiaohua's family will start from Harbin by train, which runs 70 kilometers per hour, The two trains meet?