Home
Class 12
MATHS
The maximum value of the integral int(a-...

The maximum value of the integral `int_(a-1)^(a+1)(1)/(1+x^(4))dx` is attained

A

exactly at two values of a

B

only at one value of a which is positive

C

only a one value of a which is negative

D

only at a = 0

Text Solution

Verified by Experts

The correct Answer is:
D
`f(a)=int_(a-1)^(a+1)(1)/(1+x^(4))dx`
`f'(a)=(1)/(1+(a+1)^(4))-(1)/(1+(a-1)^(4))=0" at "a=0`
`f''(0)lt0" at "a=0`
`therefore" f(a) has a local maximum at a = 0."`
Promotional Banner

Similar Questions

Explore conceptually related problems

The value of the integral int_(1)^(e ) (log x)^(2)dx is -

The value of the integral int_(0)^(1) x(1-x)^(n)dx is -

The value of the integral int_(-a)^(a)(xe^(x^(2)))/(1+x^(2))dx is

Evaluate the integrals int_(1)^(2)(1/x-1/(2x^(2)))dx

The value of the integral int_0^1e^(x^2)dx

The value of the integral int_(-1)^(1){(x^(2015))/(x^2+cosx)}dx is equal to

The value of integral int_(-1)^(1)(|x+2|)/(x+2)dx is

The value of the integral int_(-1)^(1)x|x|dx is equal to -

The value of the integral int_(0)^(2)|x^(2)-1|dx is

The value of the integral int_(1)^(2)e^(x)(log_(e)x+(x+1)/(x))dx is-