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Question

22.If-f(x) = 4x3-4such that f(2) 0. Then f(x) isdx1 129(A) 4+-129441291 1294

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Solution

The function is given as,

d dx f( x )=4 x 3 3 x 4

We have to calculate the integral of d dx f( x ) .

Use the formula of x n dx = x n+1 n+1 +A , where A is constant.

d dx f( x ) = ( 4 x 3 3 x 4 ) dx f( x )=4 x 3 dx3 x 4 dx =4 x 4 4 3 x 3 3 +D = x 4 + 1 x 3 +D (1)

It is given that f( 2 )=0,

Substitute the value of x= 2 in equation (1).

f( 2 )= ( 2 ) 4 + 1 ( 2 ) 3 +D =16+ 1 8 +D D= 129 8

Substitute the value of D in equation (1).

f( x )= x 4 + 1 x 3 129 8

Hence, option (A) is correct.


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