Home
Class 12
MATHS
If int f(x)dx=psi(x), then int x^5f(x^3)...

If `int f(x)dx=psi(x)`, then `int x^5f(x^3)dx`

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`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise Archives JEE ADVANCED (Single Correct Answer Type)|1 Videos

  • INDEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise Single Correct Answer Type|48 Videos

  • INDEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise EXERCISES (Numerical Value Type)|10 Videos

  • HYPERBOLA

    CENGAGE PUBLICATION|Exercise COMPREHENSION TYPE|2 Videos

  • INEQUALITIES AND MODULUS

    CENGAGE PUBLICATION|Exercise Single correct Answer|21 Videos

Similar Questions

Explore conceptually related problems

If intf(x)dx=Psi(x)," then "intx^(5)f(x^(3))dx is equal to -

If int f(x) dx=f(x) , then int {f(x)}^(2)dx is equal to -

If int g(x)dx = g(x) , then int g(x){f(x) - f'(x)}dx is equal to

If f(2-x)=f(2+x) and f(4-x)=f(4+x) for all x and f(x) is a function for which int_0^2 f(x)dx=5 , then int_0^(50)f(x)dx is equal to

If f(a+b-x)=f(x) , then int_(a)^(b) x f(x)dx is equal to -

Let inte^x{f(x)-f^(prime)(x)}dx=varphi(x)dot Then inte^xf(x)dx is

if f(x) is a function such that f(x+k)=f(x) for K in I^+ and I=int_0^k f(x)dx then I=int_0^(k^(2-k))f(x)dx is equal to

Evaluate:If f(a-x)=f(x), then show that int_0^axf(x)dx=a/2int_0^af(x)dx

If int(e^x-1)/(e^x+1)dx= f(x) +c, then find f(x).

If int_(-1)^4 f(x) dx =4 and int_2^4[3-f(x)]dx=7 then the value of int_(-1)^2 f(x) dx is