Home
Class 12
MATHS
Prove the following int-1^1 x^(17) cos^4...

Prove the following `int_-1^1 x^(17) cos^4x dx` = 0

Text Solution

Verified by Experts

`(-x)^(17) cos^4(-x) = -x^(17)cos^4x`
`gt x^(17) cos^4x` is an odd function.
therefore `int_-1^1 x^(17) cos^4x dx = 0`
If f(x) is an odd function, then `int_-a^a f(x) dx = 0`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATIONS

    A N EXCEL PUBLICATION|Exercise QUESTION BANK |134 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    A N EXCEL PUBLICATION|Exercise QUESTION BANK|22 Videos

Similar Questions

Explore conceptually related problems

Prove the following: int_0^1 x e^x dx = 1

Prove the following: int_1^3 dx/(x^2(x+1) = 2/3 +log(2/3)

Evaluate the following int_0^1 xe^(x^2)dx

Evaluate int_-1^1 sin^5x cos^4x dx

Using properties evaluate the following definite integrals, evaluate the following: int_0^1 x(1-x)^n dx

Evaluate the following int(1)/(x^(4)-1)dx

Evaluate the following integrals: int_-1^1 (x+1) dx

Find the following integrals int (1-sinx)/cos^2 x dx

Find the following: int 1/(x(x^7+1))dx

Evaluate the following int_(-1//2)^(1//2)cosx"log"(1-x)/(1+x)dx