Home
Class 12
MATHS
If I=intx^(27)(6x^(2)+5x+4)(x^(2)+x+1)^...

If `I=intx^(27)(6x^(2)+5x+4)(x^(2)+x+1)^(6)dx=f(x)+C`, then f(x) is equal to

A

`(x^(4)(1+x+x^(2))^(7))/(7)+C`

B

`(x^(28)(1+x+x^(2))^(7))/(7)+C`

C

`(x^(28)(1+x+x^(2))^(7))/(28)+C`

D

None

Text Solution

Verified by Experts

The correct Answer is:
B
`I=intx^(24)(1+x+x^(2))^(6).{x^(3)(4+5x+6x^(2))}dx`
`=int(x^(4)+x^(5)+x^(6))^(6).(6x^(5)+5x^(4)+4x^(3))dx`
`=(x^(28)(1+x+x^(2))^(7))/(7)+c`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Subjective Type|6 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Comprehension Type|2 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise JEE Advanced Previous Year|1 Videos

  • HYPERBOLA

    CENGAGE|Exercise JEE Advanced Previous Year|14 Videos

  • INEQUALITIES AND MODULUS

    CENGAGE|Exercise Single correct Answer|21 Videos

Similar Questions

Explore conceptually related problems

if f(x^(2))=4x^(6)+3x^(4), then f(5) is equal to

If f(x)=|x^(2)-5x+6| then f'(x) is equal to

If intx.f(x)dx=(1)/(2)f(x)+c , then f(x)=

Let f(x)=(x^(2)-x)/(x^(2)+2x) then d(f^(-1)x)/(dx) is equal to

Let f(x)=x^(8)-6x^(7)+5x^(6)+x^(4)-5x^(3)-x^(2)-3x+3AA x in R then f(5) is equal to :-

intx^6(x^3-2x^2+5)dx