Home
Class 12
MATHS
The value of I=overset(0)underset(-2)i...

The value of
`I=overset(0)underset(-2)int{x^(3)+3x^(2)+3x+3+(x+1)cos(x+1)cos(x+1)}dx`, is

A

0

B

3

C

4

D

1

Text Solution

Verified by Experts

The correct Answer is:
C
`l =int_(-2)^(0)[x^(3)+3x^(2)+3x+3+(x+1)cos(x+1)]dx`
`=int_(-2)^(0)[(x+1)^(3)+2+(x+1)cos(x+1)]dx`
Put `x+1=trArrdx=dt`
`therefore l =int_(-1)^(1)t^(3)dt+2int_(-1)^(1)dt+int_(-1)^(1)tcos t dt`
`=0+2[1-(-1)]+0`
`rArr l =4`
`[{:(becauset^(3) "and t cos t are odd functions".,),(therefore int_(-1)^(1)t^(3)dt=int_(1)^(1)t cos t dt =0,):}]`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|22 Videos

  • DEFINITE INTEGRALS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|22 Videos

  • CONTINUITY

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|16 Videos

  • DIFFERENTIAL EQUATION

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|27 Videos

Similar Questions

Explore conceptually related problems

The value of I=int_(-2)^(0){x^(3)+3x^(2)+3x+3+(x+1)cos(x+1)cos(x+1)}dx , is

underset1overset2int 3x^2dx =???

I=int_(0)^(2)(3x^(2)-3x+1)cos(x^(3)-3x^(2)+4x-2)dx

Find the value of int_(0)^(1)root(3)(2x^(3)-3x^(2)-x+1)dx

int_(-2)^(0){x^(3)+3x^(2)+3x+3+(x+1)cos(x+1)dx is equal to (A)-4(B)0(C)4(D)6

" (1) "int x^(2)*cos x^(3)dx

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-PRACTICE EXERCISE (Exercise 2) (MISCELLANEOUS PROBLEMS)
  1. int (0)^(oo) (dx)/((x+ sqrt(x^(2)+1))^(3)) is equal to

    Text Solution

    |

  2. The value of the integral int (-pi//2)^(pi//2) sqrt(cos x - cos ^(3) ...

    Text Solution

    |

  3. The value of I=overset(0)underset(-2)int{x^(3)+3x^(2)+3x+3+(x+1)cos(...

    Text Solution

    |

  4. int (alpha)^(beta) sqrt((x-alpha)/(beta -x)) dx is equal to

    Text Solution

    |

  5. Let f(x) be a function satisfyingf'(x)=f(x) withf(0) =1 and g(x) be a ...

    Text Solution

    |

  6. The value overset(2)underset(-2)int {p" In"((1+x)/(1-x))+q" In "((1-...

    Text Solution

    |

  7. Let F (x) = f(x) + f ((1)/(x)), where f (x) = int (1) ^(x ) (log t)/(1...

    Text Solution

    |

  8. If 2f(x) - 3 f(1//x) = x," then " int(1)^(2) f(x) dx is equal to

    Text Solution

    |

  9. int (0)^(2pi) sin^(6) x cos^(5) x dx is equal to

    Text Solution

    |

  10. int (-3pi//2)^(-pi//2) [ ( x + pi)^(3) + cos^(2) x ] dx is equalt to

    Text Solution

    |

  11. int (0)^(3) (3x+1)/(x^(2)+9) dx =

    Text Solution

    |

  12. underset(n to oo)lim underset(r=1)overset(n)sum(1)/(n)e^(r//n) is

    Text Solution

    |

  13. int (-1//2)^(1//2) cos x log ((1+x)/(1-x)) dx = k log 2 , then k equ...

    Text Solution

    |

  14. The value of the integral int (0)^(pi//2) sin ^(5) x dx is

    Text Solution

    |

  15. If int (0)^(x^(2)) f(t) dt = x cos pix , then the value of f(4) is

    Text Solution

    |

  16. If f(x) is differentiable and int0^(t^2)xf(x)dx=2/5t^5, then f(4/(25))...

    Text Solution

    |

  17. The value of int (0)^(pi//2) sin ^(8) x dx is

    Text Solution

    |

  18. The value of overset(pi)underset(-pi)int(1-x^(2)) sin x cos^(2) x" dx"...

    Text Solution

    |

  19. int (0)^(1) (xdx)/([x + sqrt(1-x^(2))]sqrt(1-x^(2))) is equal to

    Text Solution

    |

  20. The value of int(0)^(pi)(Sigma(r=0)^(3)a(r)cos^(3-r)x sin^(r)x)dx depe...

    Text Solution

    |