Home
Class 12
MATHS
f,g, h , are continuous in [0, a],f(a-x)...

`f,g, h ,` are continuous in `[0, a],f(a-x)=f(x),g(a-x)=-g(x),3h(x)-4h(a-x)=5.` Then prove that `int_0^af(x)g(x)h(x)dx=0`

Text Solution

AI Generated Solution

To prove that \[ \int_0^a f(x) g(x) h(x) \, dx = 0, \] we will use the properties of the functions \(f\), \(g\), and \(h\) given in the problem. ...
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION

    CENGAGE ENGLISH|Exercise CAE_TYPE|88 Videos

  • DEFINITE INTEGRATION

    CENGAGE ENGLISH|Exercise SCQ_TYPE|113 Videos

  • DEFINITE INTEGRATION

    CENGAGE ENGLISH|Exercise JEE ADVANCED|38 Videos

  • CURVE TRACING

    CENGAGE ENGLISH|Exercise EXERCISES|24 Videos

  • DETERMINANT

    CENGAGE ENGLISH|Exercise Multiple Correct Answer|5 Videos

Similar Questions

Explore conceptually related problems

If fa n dg are continuous function on [0,a] satisfying f(x)=f(a-x)a n dg(x)(a-x)=2, then show that int_0^af(x)g(x)dx=int_0^af(x)dxdot

If f\ a n d\ g are continuious on [0,\ a] and satisfy f(x)=f(a-x)a n d\ g(x)+g(a-x)=2. show that int_0^af(x)g(x)dx=int_0^af(x)dx

If fa n dg are continuous function on [0,a] satisfying f(x)=f(a-x)a n dg(x)+g(a-x)=2, then show that int_0^af(x)g(x)dx=int_0^af(x)dxdot

Let f and g be continuous fuctions on [0, a] such that f(x)=f(a-x)" and "g(x)+g(a-x)=4 " then " int_(0)^(a)f(x)g(x)dx is equal to

If f and g are continuous functions on [ 0, pi] satisfying f(x) +f(pi-x) =1=g (x)+g(pi-x) then int_(0)^(pi) [f(x)+g(x)] dx is equal to

If f(x)=(1)/((1-x)),g(x)=f{f(x)}andh(x)=f[f{f(x)}] . Then the value of f(x).g(x).h(x) is

Prove that int_(0)^(a)f(x)g(a-x)dx=int_(0)^(a)g(x)f(a-x)dx .

If f(x)=x-1, g(x)=3x , and h(x)=5/x , then f^(-1)(g(h(5))) =

Let f(x) be a continuous function AAx in R , except at x=0, such that int_0^a f(x)dx , ain R^+ exists. If g(x)=int_x^a(f(t))/t dt , prove that int_0^af(x)dx=int_0^ag(x)dx

If f,g,a n d \ h are differentiable functions of x and d(x)=|[f,g,h],[(xf)',(xg)',(x h)'],[(x^(2)f)'',(x^2g)'',(x^2h)'']| prove that d^(prime)(x)=|[f,g,h],[f',g',h'],[(x^3f' ')',(x^3g' ')',(x^3h ' ')']|

CENGAGE ENGLISH-DEFINITE INTEGRATION -SOLVED EXAMPLE_TYPE
  1. f,g, h , are continuous in [0, a],f(a-x)=f(x),g(a-x)=-g(x),3h(x)-4h(a-...

    Text Solution

    |

  2. Evaluate int(0)^((pi)/2)(sin3x)/(sinx+cosx) dx.

    Text Solution

    |

  3. Given a function f:[0,4]toR is differentiable ,then prove that for som...

    Text Solution

    |

  4. Prove that int(0)^(oo) (sin^(2)x)/(x^(2))dx=int(0)^(oo) (sinx)x dx

    Text Solution

    |

  5. If int0^(pi/2)logsinthetadtheta=k , then find the value of int0^(pi/2)...

    Text Solution

    |

  6. Evaluate : int0^pi(x^2sin2x*sin(pi/2*cosx))/(2x-pi)dx

    Text Solution

    |

  7. Find the value of int(-pi/3)^(pi/3)(pi+4x^3)/(2-cos(|x|pi/3))dx

    Text Solution

    |

  8. It is known that f(x) is an odd function and has a period p. Prove tha...

    Text Solution

    |

  9. Evaluate: int0^(pi/4)(tan^(-1)((2cos^2theta)/(2-sin2theta)))sec^2theta...

    Text Solution

    |

  10. If f(x)=(sinx)/xAAx in (0,pi], prove that pi/2int0^(pi/2)f(x)f(pi/2-x)...

    Text Solution

    |

  11. Let f(x) be a continuous function AAx in R , except at x=0, such that...

    Text Solution

    |

  12. If xint0^xsin(f(t))dt=(x+2)int0^x tsin(f(t))dt ,w h e r ex >0, then sh...

    Text Solution

    |

  13. Show that: int0^(pi//2)f(sin2x)sinxdx=sqrt(2)int0^(pi//4)f(cos2x)co...

    Text Solution

    |

  14. Let a+b=4,w h e r ea<2,a n dl e tg(x) be a differentiable function. If...

    Text Solution

    |

  15. If" f, is a continuous function with int0^x f(t) dt->oo as |x|->ooth...

    Text Solution

    |

  16. If f(x+f(y))=f(x)+yAAx ,y in R and f(0)=1, then prove that int0^2f(2-...

    Text Solution

    |

  17. Suppose f is a real-valued differentiable function defined on [1,oo] w...

    Text Solution

    |

  18. Let f be a continuous function on [a , b]dot If F(x)=(inta^xf(t)dt-int...

    Text Solution

    |

  19. f(x) is a continuous and bijective function on Rdot If AAt in R , the...

    Text Solution

    |

  20. If f(x)=x+int0^1 t(x+t) f(t)dt, then find the value of the definite in...

    Text Solution

    |