Is the integrand function in definite integral monotone? So, when a < B, the upper limit is B, the lower limit is a, the definite integral (x-x ^ 2), what value does B get when it has the maximum value

Is the integrand function in definite integral monotone? So, when a < B, the upper limit is B, the lower limit is a, the definite integral (x-x ^ 2), what value does B get when it has the maximum value

There are three conditions for function integrability: 1, continuous 2, finite discontinuities 3, monotone

Using function parity to calculate the definite integral of ∫ (upper limit π, lower limit - π) x ^ 4sinxdx
If the problem needs detailed process
∫ (upper limit π, lower limit - π) (x ^ 4) sinxdx

Let f (x) = x ^ 4sinx, then f (- x) = - x ^ 4sinx = - f (x)
So the integrand function is odd, and the integrand interval [π, - π] is symmetric about the origin
∫(π,-π)（x^4）sinxdx=0

How to calculate definite integral, upper limit π, lower limit 1, integrand 2x

∫ (upper limit π, lower limit 1) 2xdx
=X & # 178; upper limit π, lower limit 1
=π²-1

Easy (& sup2; for square and & sup3; for cube) calculation problem
1.（x+1)(x+6) 2.(-6x²）²+(-3³)·x3、(x-2y)²-(x-2y)(x+2y)-2x(2x-y).^

1. The original formula = x & sup2; + 6x + X + 6 = x & sup2; + 7x + 6
2. The original formula = 36x fourth power + (- 27) · x = 36x fourth power - 27x
3. The original formula = x & sup2; - 4xy + 4Y & sup2; - (X & sup2; - 4Y & sup2;) - (4x & sup2; - 2XY)
=-4xy+8y²-4x²+2xy
=-4x²-2xy+8y²

What is the indefinite integral XF (x ^ 2) f '(x ^ 2) DX

Just round it up, because DF (x ^ 2) = 2xf '(x ^ 2)
So ∫ XF (x ^ 2) f '(x ^ 2) DX
=1/2∫[2xf'(x^2)]*f(x^2)dx
=1/2∫f(x^2)df(x^2)
=1/2*1/2*[f(x^2)]^2+C
=1/4*[f(x^2)]^2+C
If satisfied, please accept!

According to the meaning of words, reward score is only 5
1. Describe the fierce debate and sharp words
2. Poor description
3. It takes a lot of words to describe
4. Speechless description of surprise
5. The description echoed

1. Lip gun tongue arrow
2. Not good at words
3. I'm tired of talking
4. Gaping and gaping
5. Hasten speech

After a cylinder is cut 12 cubic decimeters, it is cut into a cone with the same height as its bottom. The volume of the cone is___ Cubic centimeter

The volume of the cone is: 12 △ 2 = 6 (cubic decimeter); answer: the volume of the cone is 6 cubic decimeter

What's the answer to five nines plus an operation sign equal to 17?

(9x9-9)/9+9=17

Z = arctan (x / y), y = √ (x ^ 2 + 1), find DZ / DX

As a result, we are going to be the world's 601; and we are going to be the world's 601; Z / \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\178;) = 1 / [(2x & # 178; + 1) √ (X & # 178; + 1)] or

It is known that f (x) and G (x) satisfy g (x) + F (x) = x & nbsp; 12, G (x) - f (x) = x & nbsp; - - 12. (1) find out the expressions of functions f (x) and G (x); (2) compare the sizes of G2 (x) and G (x2); (3) find out the values of F (4) - 2F (2) g (2) and f (9) - 2F (3) g (3) respectively, thus generalize a formula that functions f (x) and G (x) hold for all real numbers x greater than 0, and prove it

(1) From the known conditions, we can get: F (x) = x12 − x − 122, G (x) = X12 + X − 122; (2) G2 (x) − g (x2) = x + 2 + X − 14 − x + X − 12 = − x − 2 + X − 14 = − (x12 − x − 12) 24 ≤ 0; ℅ G2 (x) ≤ g (x2), when x = 1, take "=; (3) f (4) - 2F (2) g (2) = 3