Home
Class 12
MATHS
Show that int(0)^(a)f(x)g(x)dx=2int(0)^(...

Show that `int_(0)^(a)f(x)g(x)dx=2int_(0)^(a)f(x)dx`, if f and g are defined as f (x) = f (a - x) and g(x) + g(a - x) = 4

Promotional Banner

Topper's Solved these Questions

  • INTEGRALS

    NCERT BANGLISH|Exercise EXERCISE 7.12|44 Videos
  • INTEGRALS

    NCERT BANGLISH|Exercise EXERCISE 7.10|10 Videos
  • DIFFERENTIAL EQUATIONS

    NCERT BANGLISH|Exercise MISCELLANEOUS EXERCISE|18 Videos
  • INVERSE TRIGONOMETRIC FUNCTIONS

    NCERT BANGLISH|Exercise MISCELLANEOUS EXERCISE|17 Videos

Similar Questions

Explore conceptually related problems

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

int_(0)^(2a)(f(x)dx)/(f(x)+f(2a-x))=a

If f(x) and g(x) be continuous in the interval [0, a] and satisfy the conditions f(x)=f(a-x) and g(x)+g(a-x)=a , then show that int_(0)^(a)f(x)g(x)dx=(a)/(2)int_(0)^(a)f(x)dx . Hence find the value of int_(0)^(pi)xsinxdx .

If f(x)=f(a-x) then int_(0)^(a)xf(x)dx is equal to

int [f(x)g"(x) - f"(x)g(x)]dx is

If f(2a-x)=-f(x) then int_(0)^(2a)f(x)dx is equal to-

The value of int_(0)^(2a) (f(x))/(f(x)+f(2a-x))dx is equal to -

Let f(x)=sin^(4)x-cos^(4)x int_(0)^((pi)/(2))f(x)dx =

Evaluate: int[f(x)g''(x)-f ''(x)g(x)]dx

Evaluate:If f(a-x)=f(x), then show that int_0^axf(x)dx=a/2int_0^af(x)dx

NCERT BANGLISH-INTEGRALS-EXERCISE 7.11
  1. By using the properties of definite integrals, evaluate the integrals ...

    Text Solution

    |

  2. By using the properties of definite integrals, evaluate the integrals ...

    Text Solution

    |

  3. By using the properties of definite integrals, evaluate the integrals ...

    Text Solution

    |

  4. By using the properties of definite integrals, evaluate the integrals ...

    Text Solution

    |

  5. By using the properties of definite integrals, evaluate the integrals ...

    Text Solution

    |

  6. int(0)^(1)x(1-x)^(n)dx

    Text Solution

    |

  7. By using the properties of definite integrals, evaluate the integrals ...

    Text Solution

    |

  8. By using the properties of definite integrals, evaluate the integrals ...

    Text Solution

    |

  9. By using the properties of definite integrals, evaluate the integrals ...

    Text Solution

    |

  10. By using the properties of definite integrals, evaluate the integrals ...

    Text Solution

    |

  11. By using the properties of definite integrals, evaluate the integrals ...

    Text Solution

    |

  12. By using the properties of definite integrals, evaluate the integrals ...

    Text Solution

    |

  13. By using the properties of definite integrals, evaluate the integrals ...

    Text Solution

    |

  14. By using the properties of definite integrals, evaluate the integrals ...

    Text Solution

    |

  15. By using the properties of definite integrals, evaluate the integrals ...

    Text Solution

    |

  16. By using the properties of definite integrals, evaluate the integrals ...

    Text Solution

    |

  17. By using the properties of definite integrals, evaluate the integrals ...

    Text Solution

    |

  18. Show that int(0)^(a)f(x)g(x)dx=2int(0)^(a)f(x)dx, if f and g are defin...

    Text Solution

    |

  19. Choose the correct answer The value of int((-pi)/2)^(pi/2)(x^(3)+xco...

    Text Solution

    |

  20. Choose the correct answer The value of int(0)^(pi/2)log((4+3sinx)/(4...

    Text Solution

    |