If f\ a n d\ g are continuious on [0,\ a...

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`

CONTINUITY
RD SHARMA ENGLISH|Exercise All Questions|282 Videos
DERIVATIVES AS A RATE MEASURER
RD SHARMA ENGLISH|Exercise All Questions|168 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 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

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

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

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

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(2a-x)=-f(x), prove that int_0^(2a)f(x)dx=0

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

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 R and f(0)=1, then prove that int_0^2f(2-x)dx=2int_0^1f(x)dx .