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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."`
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