If f(x) is continuous and int(0)^(9)f(x)...

If f(x) is continuous and `int_(0)^(9)f(x)dx=4`, then the value of the integral `int_(0)^(3)x.f(x^(2))dx` is

A

2

B

18

C

16

D

4

Verified by Experts

The correct Answer is:

A

Let `I=int_(0)^(3)x.f(x^(2))dx`
Put `x^(2)=t`
`rArr" "2x.dx=dt`
`rArr" "I=(1)/(2)int_(0)^(9)f(t)dt=(1)/(2).4=2`

Similar Questions

Explore conceptually related problems

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

The value of the integral int_(0)^(pi//2)(f(x))/(f(x)+f(pi/(2)-x))dx is

The value of integral int _(0)^(pi) x f (sin x ) dx is

The value of the integral int_(0)^(2a) (f(x))/(f(x)+f(2a-x))dx is equal to

If f(x)-3cos(tan^(-1)x) , then the value of the integral int_(0)^(1)xf''(x)dx is

If f(x) is a continuous function satisfying f(x)=f(2-x) , then the value of the integral I=int_(-3)^(3)f(1+x)ln ((2+x)/(2-x))dx is equal to

If f(0)=1,f(2)=3,f'(2)=5 ,then the value of the definite integral int_(0)^(1)xf''(2x)dx is

int_(0)^( If )(f(t))dt=x+int_(x)^(1)(t^(2)*f(t))dt+(pi)/(4)-1 then the value of the integral int_(-1)^(1)(f(x))dx is equal to

If f(x) is a continuous function in [0,pi] such that f(0)=f(x)=0, then the value of int_(0)^(pi//2) {f(2x)-f''(2x)}sin x cos x dx is equal to

If f(k - x) + f(x) = sin x , then the value of integral I = int_(0)^(k) f(x)dx is equal to