Home
Class 12
MATHS
Evaluate int(0)^(2)x (2-x)^ndx...

Evaluate `int_(0)^(2)x (2-x)^ndx`

Text Solution

Verified by Experts

The correct Answer is:
C
`int_(0)^(x)|sint|dt=int_(0)^(2npi)|sint|dt+int_(2npi)^(x)|sint|dt`
`=2nint_(0)^(pi) |sint|dt+int_(2npi)^(x)sin tdt`
(as `x` lies in either first or second quadrant)
`=2n(-cost)_(0)^(pi)+(-cost)_(2npi)^(x)=4n-cosx+1`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION

    CENGAGE|Exercise Exercise (Multiple)|27 Videos

  • DEFINITE INTEGRATION

    CENGAGE|Exercise Exercise (Comprehension)|31 Videos

  • DEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 8.11|6 Videos

  • CURVE TRACING

    CENGAGE|Exercise Exercise|24 Videos

  • DETERMINANT

    CENGAGE|Exercise Multiple Correct Answer|5 Videos

Similar Questions

Explore conceptually related problems

Evaluate int_(0)^(2)x(2-x)^3dx

Evaluate int_(0)^(1) x e^(-2x) dx

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

Evaluate int_(0)^(2)(x^2+x+2)dx

Evaluate int_(0)^(3)(x^2-6x+5)dx

Evaluate int_(0)^(1)e^(2-3x)dx

Evaluate int_(0)^(2)7^(x)dx .

Evaluate int_(0)^(2)(2x+1)dx as limit of a sum

Evaluate int_(0)^(2)(3x^(2)-4x+5)dx

Evaluate int_(0)^(4)(x^2+2x+8)dx

CENGAGE-DEFINITE INTEGRATION -Exercise (Single)
  1. ("lim")(xvec1)1/(sqrt(|x|-{-x}))(w h e r e{x} denotes the fractional ...

    Text Solution

    |

  2. The value of int0^x[cost]dt ,x in [(4n+1)pi/2,(4n+3)pi/2]a n dn in N ...

    Text Solution

    |

  3. Evaluate int(0)^(2)x (2-x)^ndx

    Text Solution

    |

  4. int0^x(2^t)/(2^([t]))dt ,w h e r e[dot] denotes the greatest integer f...

    Text Solution

    |

  5. If intsinx d(secx)=f(x)-g(x)+c ,t h e n f(x)=secx (b) f(x)=tanx g(x...

    Text Solution

    |

  6. Ifg(x)=int0^x(|sint|+|cost|)dt ,t h e ng(x+(pin)/2) is equal to, wher...

    Text Solution

    |

  7. Ifx=intc^(sint)sin^(-1)z dz ,y=intk^(sqrt(t))(sinz^2)/zdz ,t h e n(dy)...

    Text Solution

    |

  8. about to only mathematics

    Text Solution

    |

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

    Text Solution

    |

  10. If f(x)=cosx-int0^x(x-t)f(t)dt ,t h e nf^(prime)(x)+f(x) is equal to -...

    Text Solution

    |

  11. A function f is continuous for all x (and not everywhere zero) such th...

    Text Solution

    |

  12. (lim)(nvecoo)1/x[inty^a e^sin^(2t)dt-int(x+y)^a e^sin^(2t)dt-]i se q u...

    Text Solution

    |

  13. Let f(x) = sqrt(log(10)x^(2)).Find the set of all values of x for whi...

    Text Solution

    |

  14. If int(0)^(x) f ( t) dt = x + int(x)^(1) tf (t) dt , then the value of...

    Text Solution

    |

  15. Iff(x)=1+1/xint1^xf(t)dt ,t h e nt h ev a l u eof(e^(-1))i s 1 (b) 0 ...

    Text Solution

    |

  16. If [f((sqrt(3))/2)] is [.] denotes the greatest integer function) 4 (b...

    Text Solution

    |

  17. f(x) is continuous function for all real values of x and satisfies int...

    Text Solution

    |

  18. The value of int(1/e)^(tanx)(tdt)/(1+t^2)+int(1/e)^(cotx)(dt)/(t(1+t^2...

    Text Solution

    |

  19. underset(xtooo)lim(x^(2)"tan"(1)/(x))/(sqrt(8x^(2)+7x+1)) is equal to

    Text Solution

    |

  20. A function f is defined by f(x) = int0^pi cos t cos(x-t)dt,0 <= x <= 2...

    Text Solution

    |