Home
Class 12
MATHS
If fa n dg are continuous function on [0...

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`

Text Solution

Verified by Experts

The correct Answer is:
NA
`int_(0)^(a)f(x)g(x)dx`
`=int_(0)^(a)f(a-x)g(a-x)dx`
`=int_(0)^(a)f(x).{2-g(x)}dx`
`=2int_(0)^(a)f(x)dx-int_(0)^(a)f(x)g(x)dx`
or `2int_(0)^(a)f(x)f(x)dx=2int_(0)^(a)f(x)dx`
or `int_(0)^(a)f(x)g(x)dx=int_(0)^(a)f(x)dx`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 8.6|7 Videos

  • DEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 8.7|6 Videos

  • DEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 8.4|10 Videos

  • CURVE TRACING

    CENGAGE|Exercise Exercise|24 Videos

  • DETERMINANT

    CENGAGE|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)+g(a-x)=2, then show that int_0^af(x)g(x)dx=int_0^af(x)dxdot

If f(x)=f(a+x) then show that int_(0)^(2a)f(x)dx=2int_(0)^(a)f(x)dx .

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 a continuous function f on [0, a] satisfies f(x)f(a-x)=1, a >0, then find the value of int_0^a(dx)/(1+f(x))

If f(x+f(y))=f(x)+yAAx ,y in Ra n df(0)=1, then prove that int_0^2f(2-x)dx=2int_0^1f(x)dxdot

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

A continuous real function f satisfies f(2x)=3(f(x)AAx in RdotIfint_0^1f(x)dx=1, then find the value of int_1^2f(x)dx

A continuous real function f satisfies f(2x)=3(f(x)AAx in RdotIfint_0^1f(x)dx=1, then find the value of int_1^2f(x)dx

If f(x)=(sinx)/xAAx in (0,pi], prove that pi/2int_0^(pi/2)f(x)f(pi/2-x)dx=int_0^pif(x)dx