Home
Class 12
MATHS
Prove that \int{-a}^a f(x) dx = 0, if f(...

Prove that `\int_{-a}^a` f(x) dx = 0, if f(x) is odd function,
=2`\int_{0}^a` f(x) dx, if f(x) is an even function

Promotional Banner

Topper's Solved these Questions

  • Definite integration

    CHETANA PUBLICATION|Exercise Exercise|111 Videos

  • BINOMIAL DISTRIBUTION

    CHETANA PUBLICATION|Exercise EXERCISE|108 Videos

  • DIFFERENTIAL EQUATIONS

    CHETANA PUBLICATION|Exercise EXERCISE|254 Videos

Similar Questions

Explore conceptually related problems

Prove that \int_{a}^b f(x) dx = - \int_{b}^a f(x) dx

Prove that \int_{0}^a f(x) dx = \int_{0}^a f(a-x) dx

Prove that \int_{a}^b f(x) dx = \int_{a}^b f(t) dt

Prove that \int_{a}^b f(x) dx = \int_{a}^b f(a+b-x) dx

Prove that \int_{a}^b f(x) dx = \int_{a}^c f(x) dx + \int_{c}^b f(x) dx , a < c < b

Prove that \int_{0}^(2a) f(x) dx = \int_{0}^a [f(x) + f(2a-x)] dx

If int_(-1)^(1)f(x)dx=0 then

int [f(x)+xf'(x)]dx =

Prove that int_(a)^(b)f(x)dx=(b-a)int_(0)^(1)f((b-a)x+a)dx

CHETANA PUBLICATION-Definite integration-Exercise
  1. Evaluate \int{0}^(pi) frac{x sin x}{1+sin x} dx

    Text Solution

    |

  2. Evaluate \int{0}^(pi) frac{x}{a^2 cos^2 x + b^2 sin^2 x} dx

    Text Solution

    |

  3. Prove that \int{-a}^a f(x) dx = 0, if f(x) is odd function, =2\int{0}...

    Text Solution

    |

  4. evaluate \int{0}^((pi)/2) frac{sin x}{sin x+ cos x} dx

    Text Solution

    |

  5. Evaluate: \int{-a}^a sqrt (frac {a-x}{a+x}) dx

    Text Solution

    |

  6. Evaluate: \int{0}^((pi)/2) cos^2 x dx

    Text Solution

    |

  7. \int{2}^3 frac{dx}{x(x^3 -1)}=.............. (A) 1/3 log(208/189) (B)...

    Text Solution

    |

  8. \int{0}^((pi)/2)frac{sin^2 x dx}{(1+cos x)^2}=........... A) frac{4-p...

    Text Solution

    |

  9. \int{0}^log 5 frac{e^x sqrt (e^x -1)}{e^x + 3} dx=........... A) 3+2p...

    Text Solution

    |

  10. \int{0}^((pi)/2) sin^6 x cos^2 x dx=............. (A) frac{7pi}{256} ...

    Text Solution

    |

  11. \int{0}^1 frac{dx}{sqrt (1+x) - sqrt x} = k/3, then k is equal to........

    Text Solution

    |

  12. \int{1}^2 frac{1}{x^2} e^(1/x) dx =................ A) sqrt e +1 B) s...

    Text Solution

    |

  13. \int{2}^a[1/log x - 1/(log x)^2] dx = a + b/ log 2 A) a=e, b=-2 B) ...

    Text Solution

    |

  14. Let I1= \int{e}^ {e^2} dx/log x and I2= \int{1}^2 frac{e^x}{x} dx, th...

    Text Solution

    |

  15. \int{0}^9 frac{sqrt x}{ sqrt x + sqrt (9-x)} dx=............. A) 9/2 B...

    Text Solution

    |

  16. The value of \int{-pi/4}^(pi/4) log( frac{2+sin theta }{2-sin theta}) ...

    Text Solution

    |

  17. The value of I=\int{0}^(pi/2) frac{1}{1+cot x} dx is........... A) pi...

    Text Solution

    |

  18. The value of \int{0}^(pi) frac{x}{4 cos^2 x + 9 sin^2 x} dx is...........

    Text Solution

    |

  19. The value of \int{0}^1 x(1-x)^99 dx is........... A) 1/10100 B) 11/1...

    Text Solution

    |

  20. The value of \int{-pi/2}^(pi/2) x sqrt (cos x - cos^2 x) dx is...........

    Text Solution

    |