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If f(x) is defined on [-2, 2] by f(x) = ...

If f(x) is defined on `[-2, 2]` by `f(x) = 4x^2 – 3x + 1 and g(x) = (f(-x)-f(x))/(x^2+3)` then `int_(-2)^2 g(x) dx` is equal to

A

64

B

`-48`

C

0

D

24

Text Solution

Verified by Experts

The correct Answer is:
C
Given , ` f(x) = 4x^(2) - 3x + 1, g(x) = (f(-x)-f(x))/(x^(2)+3)`
` :. g(x) = ((4x^(2) +3x+1)-(4x^(2)-3x+1))/(x^(2)+3) = (6x)/(x^(2)+3)`
Now, ` g(-x) = - (6x)/(x^(2)+3) = - g(x)`
Which is an odd function
` :. int _(-2)^(2) g(x) dx = 0`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-MHT CET Corner
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