Home
Class 12
MATHS
int(-2)^(0){x^(3)+3x^(2)+3x+3+(x+1)cos(x...

`int_(-2)^(0){x^(3)+3x^(2)+3x+3+(x+1)cos(x+1)} dx` is equal to

A

0

B

3

C

4

D

1

Text Solution

Verified by Experts

The correct Answer is:
C
We have,
`I=overset(0)underset(-2)int{x^(3)+3x^(2)+3x+3+(x+1)cos(x+1)cos(x+1)}dx`
`rArr I=overset(0)underset(-1)int {(x+1)^(3)+2+(x+1)cos(x+1)}dx`
`rArr I=overset(0)underset(-1)int (t^(3)+2+tcost)dt`, where t=x+1
`rArr I=overset(1)underset(-1)int t^(3)dt+overset(1)underset(-1)int 2dt+overset(1)underset(-1)int tcos dt `
`rArr I=0+2xx2+0=4`
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

int(x^(3))/(x+1)dx is equal to

int_(0)^(3)(x^(2)+1)dx

1. int_(0)^(2)3x^(2)dx

The value of int _(0)^(1) ((x ^(6) -x ^(3)))/((2x ^(3)+1)^(3)) dx is equal to :

The value of int_(-1)^(1)(sin^(-1)x+(x^(5)+x^(3)-1)/(cos^(2)x))dx is equal to

int(x+2)/((x^(2)+3x+3)sqrt(x+1))dx " is equal to"

int_(-3)^(3)(x^(2))/((x^(2)+3)(1+e^(x)))dx is equal to

int_(0)^(1) (1)/(x^(2) +2x+3)dx

int_(lnpi-ln2)^(lnpi) (e^(x))/(1-cos(2/3e^(x))) dx is equal to

int_(1)^(9)(x^((3)/(2))+2x+3)dx

OBJECTIVE RD SHARMA ENGLISH-DEFINITE INTEGRALS-Chapter Test 2
  1. int(-2)^(0){x^(3)+3x^(2)+3x+3+(x+1)cos(x+1)} dx is equal to

    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

    |