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Calculation by using definite integral characteristic of periodic function ∫ (upper n π lower 0) | sinx| DX
Because this formula is the integral of absolute value, according to the properties of sine function, it is greater than or equal to 0 from 0 to π, so it can be changed into
N * ∫ (upper π lower 0) sinxdx
=N * (- cosx) | (upper π, lower 0)
=2n
That's it!
1. If the integrand is continuous, the indefinite integral must exist. 2. If a bounded function is multiplied by an infinitesimal, it is still an infinitesimal
3. The geometric meaning of indefinite integral is an integral curve
4. The derivative of any infinitesimal is infinitesimal
F (x) = 0 is infinitesimal, so is the derivative
Judgment question: the basic requirement of definite integral is that the integrand domain is finite and the integrand function is bounded. Is it right or wrong?
Correct, if the integrand domain is infinite and the integrand function is unbounded, then it is an abnormal integral
Who can tell me in vernacular what is the positive and negative proportion? It's better to give some examples
A positive proportion is an increase. Another one related to it will increase with it
Inverse proportion is an increase, and the other related to it will decrease
For example, if you put a 2 meter long wooden pole in the sun at the same time, the shadow length will be 3 meters, but if you put a 3 meter long pole in one place, the shadow length will be 5 meters
After the introduction of negative numbers, numbers can be divided into "two kinds of quantities with opposite meanings"?
What are the categories
A: it can be divided into three categories
9. Divide the nine numbers 39, 45, 49, 56, 60, 70, 78, 84 and 91 into three groups so that the product of the three numbers in each group is equal
1.45 56 91
2.60 78 49
3.70 84 39
Because there are three large prime numbers 39, 49 and 91 in the above nine numbers, we can't use decomposition prime number to analyze them
The first step is to analyze the parity of the bits of each number, five even numbers (two zeros, one 6, 8, 4), four odd numbers (one five, two nines, one one). Since five and even numbers can form even numbers, the bits of the product of three numbers are even numbers
In the second step, we know that the number of bits is even, and because there are two zeros, if two zeros are in a group, then the number of bits is zero, another group has five and even number can also be zero, but no matter how the third group is combined, it is impossible to be zero (4, 6, 8, any two can not have zero). Therefore, we can know that 45, 60, 70 are in three groups
In the third step, because the products of the three numbers are equal, 78,84,91 of the remaining 39,49,56,78,84,91 must be different in one group. Similarly, 39,49,56 must not be in the same group. They are composed of six groups: A, 3991 4984 5678; B, 3991 4978 5684; C, 3984 4991 5678; D, 3984 4978 5691; E, 3978 4984 5691; F, 3978 4991 5684, They are combined with 45, 60 and 70 respectively, and 9 and 45 cannot be combined. Otherwise, the number of bits is odd, and the ten bits of them combined with 60 and 70 must be equal. It can be seen that only groups B, D, e and F are possible. There are six combinations of 60 and 9, 70 and 2, or 60 and 6, 70 and 2
a 603991 704978 455684
b 604991 703978 455684
c 603984 704978 455691
d 605691 704978 453984
e 604984 703978 455691
f 605691 703978 454984
From this, we can judge that the number one or three of D is obviously not equal
The rest can only be calculated and confirmed
1000 mu = how many square meters
Conversion of Mu and M2 units
How many square meters is an acre equal to
666.666...*1000=666666.666...
Translation of unit 3a in Grade 9 English volume 1
How do you learn English well? This week we asked students about the best way to learn English in Xinxing high school. Many students said that they have learned English. Some students have more specific suggestions. Lillian Li, for example, the best way to learn new words is to read
Least common multiple of 12 and 14
84
The ratio of 1 / 2 to 1 / 5 is equal to 1 / 4 to X
One in two to one in five equals one in four to X
1/2*x=1/5*1/4
x=(1/20)/(1/2)
x=1/10
RELATED INFORMATIONS
- 1. The definite integral exists. There are finite discontinuities on AB and they are bounded. Are discontinuities all kinds of discontinuities
- 2. The definite integral of the product of integrable functions is equal to the product of their respective definite integrals A right B wrong
- 3. If the integrand is continuous, must its definite integral be continuous?
- 4. Definite integral of piecewise function f(X)={ sinX (0
- 5. How to solve the problem of definite integral of even function? Remember there is an example that we should pay attention to the symmetric interval for definite integral. If we directly solve it, we will get the wrong result. We need to use the law of even times odd zero to solve it. Can we give such an example?
- 6. How to prove that the function f (x) = 2sinx-x + 1 is continuous on the closed interval [0,3]? Such as the title
- 7. A function problem in Higher Mathematics If a company produces a product and can sell it all, the revenue function is r = 36x-x quadratic / 20, where x is the daily production of the company. If the daily production of the company increases from 250 to 260, please estimate the increase of the company's revenue It's necessary to explain the text and the steps, We should use the function method of higher mathematics, not the method of elementary school, complete steps, instructions and results
- 8. What are the definitions of bounded and unbounded functions and how to judge whether a function is bounded or unbounded? Let me start with a few questions 1. Is f (x) ∈ (a, b), f (x) bounded? G (x) ∈ [a, b], the upper bound of G (x) is B, the lower bound is a, which should be right 2. Functions with limits are not necessarily bounded? For example 3. Does f (x) unbounded represent f (x) →∞ when x ∈ (a, b), or other?
- 9. Definition of bounded function and unbounded function? Are some functions with lower bounds, such as quadratic function of y = x ^ 2, unbounded functions
- 10. Is unbounded function multiplied by bounded function or unbounded function?
- 11. The definite integral of periodic function on (a, a + T) has nothing to do with A. how to prove it? The definite integral of periodic function on (a, a + T) has nothing to do with A. how to prove it? F (x) = f (x + T). Find the definite integral of F (x) on [a, a + T]. The conclusion is that the definite integral is a definite value, that is, the definite integral of F on [0, t].
- 12. If the function f (x) defined on [a, b] is greater than 0, then its definite integral on [a, b] must be greater than 0? May it be equal to 0? Your answer is incorrect, because f (x) is not necessarily a continuous function. I already know how to prove it It's my first time to ask a question and see how quickly you reply to me,
- 13. If the function f (x) is defined on [a, b] and | f (x) | is integrable on [a, b], does the integral of F (x) exist on [a, b]?
- 14. How to prove that a function is unbounded on an interval Prove that y = 1 / X sin1 / X is unbounded on (0,1]
- 15. The continuity of higher number function (concrete process) f(X)=1/xsinx,(x0) When we ask what the constant k is, f (x) is continuous in its domain?
- 16. Continuity of functions in higher numbers Discuss the continuity of the following functions and draw the f (x) graph 1. F (x) = LIM (n approaches infinity) 1 (1 + (cosx) ^ 2n) 2. F (x) = LIM (n approaches infinity) {[1-x ^ (2n)] \ [1 + x ^ (2n)]} * x Graphic words, a little description of what it looks like
- 17. Rolle's theorem, Lagrange's mean value theorem and Cauchy's mean value theorem are generally applied to what questions?
- 18. The relationship between Lagrange's mean value theorem and Rolle's theorem
- 19. The difference between the function differentiable in the closed interval and the function differentiable in the closed interval, why is the mean value theorem only required to be differentiable in the open interval? Why do mean value theorems only require derivability in open intervals? Closed interval is continuous, open interval is differentiable, so closed interval is differentiable? Explain why... I need a reason
- 20. Zero point theorem and intermediate value theorem