Home
Class 12
MATHS
If intx^2dote^(-2x)dx=e^(-2x)(a x^2+b x+...

If `intx^2dote^(-2x)dx=e^(-2x)(a x^2+b x+c)+d ,` then the value of `|a/(b c)|` is______

A

`a= -(1)/(2)`

B

`b =(1)/(2)`

C

`c= -(1)/(4)`

D

`d in R`

Text Solution

Verified by Experts

The correct Answer is:
A, C, D
`intx^(2)e^(-2x)dx=e^(-2x)(ax^(2)+bx+c)+d`
Differentiating both sides, we get
`x^(2)e^(-2x)=e^(-2x)(2ax+b)+(ax^(2)+bx+c)(-2e^(-2x))`
`=e^(-2x)(-2ax^(2)+2(a-b)x+b-2c)`
`or a=(-1)/(2),2(a-b)=0,b-2c=0`
` or b=(-1)/(2),c=(-1)/(4)`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise (Comprehension)|17 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise (Matrix)|4 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise (Single)|77 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

intx^(2)e^(2x)dx is:

Let A=[[3x^2], [1], [6x]],B=[a,b,c] and C=[[(x+2)^2, 5x^2, 2x],[5x^2, 2x,(x+2)^2],[ 2x,(x+2)^2, 5x^2]] be three given matrices, where a ,b ,ca n dx in Rdot Given that tr(AB)=tr(C). If f(x)=a x^2+b x+c , then the value of f(1) is ______.

If int (x^(8)-12x^(4)+4)/(x^(4)-4x^(2)+2)dx = x^(a)/a + (4x^(b))/b +2x+C , then the value of (a+b) is

intx^(2)e^(x^(3))dx equals

If: ("lim")_(xrarr1)(1+a x+b x^2)^(c/((x-1)))=e^3, then the value of b c is___

If int f' (x) e^(x^(2)) dx = (x-1)e^(x^(2)) + c , then f (x) is

If f(x) =(e^x)/(1+e^x), I_1=int(f(-a))^(f(a)) xg(x(1-x)dx, and I_2=int_(f(-a))^(f(a)) g(x(1-x))dx, then the value of (I_2)/(I_1) is (a) -1 (b) -2 (c) 2 (d) 1