Let f (x) be continuous in [- B, b], and prove that the definite integral [- B, 0] f (x) DX = the definite integral [0, b] f (- x) DX

Let f (x) be continuous in [- B, b], and prove that the definite integral [- B, 0] f (x) DX = the definite integral [0, b] f (- x) DX

Let y = - x;
[0,b]f(-x)dx=
-[0,b]f(-x)d(-x)=
[b,0]f(-x)d(-x)=
[b,0]f(y)dy=[-b,0]f(x)dx
The last step is to use the integral invariance of one variable function

Given the first-order function y = x + 1, ask which quadrants the image passes through, and find the area of the triangle formed by the image of the first-order function and the X, Y axes

Area: let y = 0 get x = - 1, let x = 0, y = 1, so s = 1 / 2, xy = 1 / 2

It is known that if the image of a linear function y = KX + B passes through points a (0, a), B (- 1,2), then the area of △ AOB is 2
Write out a function analytic formula that meets the condition

A(0,-2)
y=-4x-2

There is a three digit number, each of which is a different prime number, and these three numbers can be divided by 3 and 5 at the same time. What are they?

735

The fast and slow trains start from the two cities at the same time, and meet at 18 kilometers away from the midpoint after 4 hours?

(70 × 4-18 × 2) △ 4, = (280-36) △ 4, = 244 △ 4, = 61 (km); a: the local train runs 61 km per hour

ABCD are all positive numbers (a + b) (c + D) > AB + CD why

Let a = b = 1, C = D = 6, left = 24, right = 37, the inequality is not tenable, is there a problem?

One ton of coal has four fifths of a ton. It takes one twentieth of a ton. How many tons? Please answer quickly. I need it urgently,

4 / 5 × 1 / 20 = 1 / 25 tons

Why should mean inequality emphasize one positive, two definite, three-phase and so on? Now I'm very depressed about this!

For example, (a + b) / 2 > = √ ab
One positive: A, B are not negative to be tenable. Tenable condition should be emphasized of course
Second determination: usually only one side is a fixed value, can we get the final result. Only when we understand this, can we know the correct direction. If it is not a fixed value, we can not get a constant result, which is usually meaningless
Third class: only when a = B, the inequality can take the equal sign. Especially in many applications, we must pay attention to the same conditions for taking the equal sign

The length of the railway between a and B is 1225 km. The two trains leave from the two places at the same time and run in opposite directions. After five hours of meeting, it is known that one train runs every hour on average
Travel 117 kilometers per hour, the average number of kilometers per hour of another bus is solved by equation

The other train is x kilometers per hour
（117+X）×5=1225
117+X=245
X = 128 km / h
The other train is 128 kilometers per hour

The basic inequality of the first year of senior high school,
1. If x > 0, find the maximum value of 2-3x-4 / x, and find the value of X
2. Given 00, x + 3Y = 1, find the minimum value of 1 / x + 1 / Y and the value of X, y
5. We know that x, y ∈ R, and X + 2Y = 1, prove that XY ≤ 8, and point out the condition of equal sign
9. When x > 1, find the minimum value of the algebraic formula (2x ^ 2-2x + 1) / (x-1) to obtain the minimum value of X
Even if I can't do basic inequality, how many can I do

1.3x + 4 / x > = 2 radical (3x * 4 / x) = 4 radical 3,
SO 2 - (3x + 4 / x) = 2 radical (2 ^ A * 2 ^ b) = 2 radical (2 ^ (a + b)) = 2 radical (2 ^ 3) = 4 radical 2
Now 2 ^ a = 2 ^ B, a = B, a = b = 3 / 2
4. Cauchy
(1 / x + 1 / y) (x + 3Y) > = (radical (1 / X * x) + radical (1 / y * 3Y)) ^ 2 = (1 + radical 3) ^ 2
In this case, X / (1 / x) = 3Y / (1 / y), x ^ 2 = 3Y ^ 2, x = radical 3 * y, y = 1 / (3 + radical 3), x = radical 3 * y = 1 / (radical 3 + 1)
5.1 = x + 2Y > = 2 radical (x * 2Y) = 2 radical 2 * radical (XY) square
xyx=1/2,y=1/4
9. (2x ^ 2-2x + 1) / (x-1), let t = X-1 > 0 = (2t ^ 2 + 2T + 1) / T = 2T + 2 + 1 / T = 2 + 2T + 1 / T > = 2 + 2 radical (2t * 1 / T) = 2 + 2 radical 2
In this case, 2T = 1 / T, t = radical 2 / 2 (rounding off negative value), x = 1 + radical 2 / 2