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If int f(x) dx = psi(x), "then" int x^(5...

If `int f(x) dx = psi(x), "then" int x^(5)f(x)` dx is equal to

A

` (1)/(3)[x^(3)Psi(x^(3))-int x^(2) Psi(x^(3))dx]+c`

B

` (1)/(3)x^(3)Psi(x^(3))-3int x^(3) Psi(x^(3))dx+c`

C

` (1)/(3)x^(3)Psi(x^(3))-int x^(2) Psi(x^(3))dx+c`

D

` (1)/(3)[x^(3)Psi(x^(3))-int x^(3) Psi(x^(3))dx]+c`

Text Solution

Verified by Experts

The correct Answer is:
C
` "Given that " int f(x)dx=Psi(x). " Let " I=int x^(5)f(x^(3))dx`
`"or " I=int t f(t)(dt)/(3) " " ("Put " x^(3)=t)`
`=(1)/(3)[t Psi(t)-int Psi(t)dt]+c`
` :. I=(x^(3))/(3) Psi(x^(3))-(1)/(3)int3x^(2)Psi(x^(3))dx+c`
`=(x^(3))/(3)Psi(x^(3))-int x^(2) Psi(x^(3))dx+c`
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