Home
Class 12
MATHS
The value of int0^1 4x^3{(d^2)/(dx^2)(1...

The value of `int_0^1 4x^3{(d^2)/(dx^2)(1-x^2)^5}dx` is

A

1

B

2

C

8

D

4

Text Solution

Verified by Experts

The correct Answer is:
B
Let `I=overset(1)underset(0)int 4x^(3){(d^(2))/(dx^(2))(1-x^(2))^(5)}dx`
`I=[4x^(3)(d)/(dx)(1-x^(2))^(5)]_(0)^(1)-overset(1)underset(0)int 12x^(2){(d)/(dx)(1-x^(2))^(5)}dx`
`rArr I=[4x^(3)xx(-10x)(1-x^(2))^(4)]_(0)^(1)-12[[x^(2)(1-x^(2))^(5)]_(0)^(1)-overset(1)underset(0)int 2x(1-x^(2))^(5)dx]`
`rArr I=0-12[0+overset(1)underset(0)int (1-x^(2))^(5)(-2x)dx]`
`rArr I=-12[((1-x^(2))^(6))/(6)]_(0)^(1)=-12(0-(1)/(6))=2`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section I - Solved Mcqs|145 Videos

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|12 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|87 Videos

  • DERIVATIVE AS A RATE MEASURER

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|26 Videos

Similar Questions

Explore conceptually related problems

The value of int_0^(2) (3x ^ 2 −1)dx

The value of int_0^1(x^4(1-x)^4)/(1+x^2)\ dx is

The value of int_(0)^(1) (1)/(2x-3)dx is

int_0^4(x^4+3x^2-1)/x^2dx

The value of int_0^1tan^(-1)((2x-1)/(1+x-x^2))dx ,\ is a. 1 b. -1 c. 0 d. pi//4

int_0^1 x^5sqrt((1+x^2)/(1-x^2))dx

The value of int_0^1(2x^2+3x+3)/((x+1)(x^2+2x+2))dx is

The value of int_0^1 (2^(2x+1)-5^(2x-1))/(10^(x))dx is

The value of int_0^1(x^4(1-x)^4)/(1+x^2)dx is/are (a) (22)/7-pi (b) 2/(105) (c) 0 (d) (71)/(15)-(3pi)/2

int_0^1 x(1-x)^(5/2) dx

OBJECTIVE RD SHARMA ENGLISH-DEFINITE INTEGRALS-Chapter Test 2
  1. The value of int0^1 4x^3{(d^2)/(dx^2)(1-x^2)^5}dx is

    Text Solution

    |

  2. The value of the integral int(0)^(2)x[x]dx

    Text Solution

    |

  3. The value of integral sum (k=1)^(n) int (0)^(1) f(k - 1+x) dx is

    Text Solution

    |

  4. Let f (x) be a function satisfying f(x)=f(x) with f(0) = 1 and g be th...

    Text Solution

    |

  5. If I=int(0)^(1)cos(2 cot^(-1)sqrt(((1-x)/(1+x))))dx then :

    Text Solution

    |

  6. The value of int(a)^(a+(pi//2))(sin^(4)x+cos^(4)x)dx is

    Text Solution

    |

  7. The vaue of int(-1)^(2) (|x|)/(x)dx is

    Text Solution

    |

  8. The value of int0^1 (x^(3))/(1+x^(8))dx is

    Text Solution

    |

  9. The value of int(0)^(3) xsqrt(1+x)dx, is

    Text Solution

    |

  10. Evaluate int(0)^(1)log(sin((pix)/(2)))dx

    Text Solution

    |

  11. Evaluate int(0)^(pi) xlog sinx dx

    Text Solution

    |

  12. If I(1)=int(0)^(oo) (dx)/(1+x^(4))dx and I(2)=underset(0)overset(oo)i...

    Text Solution

    |

  13. If f(x)={{:(x,xlt1),(x-1,xge1):}, then underset(0)overset(2)intx^(2)f(...

    Text Solution

    |

  14. The value of the integral overset(1)underset(0)int (1)/((1+x^(2))^(3//...

    Text Solution

    |

  15. Prove that: int0^(2a)f(x)dx=int0^(2a)f(2a-x)dxdot

    Text Solution

    |

  16. If int(0)^(36) (1)/(2x+9)dx =log k, is equal to

    Text Solution

    |

  17. The value of the integral int(0)^(pi//2) sin^(6) x dx, is

    Text Solution

    |

  18. If int(0)^(oo) e^(-x^(2))dx=sqrt((pi)/(2))"then"int(0)^(oo) e^(-ax^(2)...

    Text Solution

    |

  19. The value of the integral int 0^oo 1/(1+x^4)dx is

    Text Solution

    |

  20. The value of alpha in [0,2pi] which does not satify the equation int(p...

    Text Solution

    |

  21. lim(x to 0)(int(0)^(x^(2))sinsqrt(t) dt)/(x^(3)) is equl to

    Text Solution

    |