If `f(a+b-x)=f(x),` then prove that `int_a^b xf(x)dx=(a+b)/2int_a^bf(x)dxdot`

If f(a+b-x0=f(x) , then prove that int_a^b xf(x)dx=((a+b)/2)int_a^bf(x)dxdot

If f(a+b-x)=f(x), then prove that int_(a)^(b)xf(x)dx=(a+b)/(2)int_(a)^(b)f(x)dx

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

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

If f(a+b-x)=f(x),\ t h e n\ int_a^b xf(x)dx is equal to (a+b)/2int_a^bf(b-x)dx b. (a+b)/2int_a^bf(b+x)dx c. (b-1)/2int_a^bf(x)dx d. (a+b)/2int_a^bf(x)dx

int_a^b[d/dx(f(x))]dx

If f(a+b-x)=f(x) , then int_a^b x f(x)dx is equal to (A) (a-b)/2int_a^b f(a+b-x)dx (B) (a+b)/2int_a^b f(b-x)dx (C) (a+b)/2int_a^b f(x)dx (D) (b-a)/2int_a^b f(x)dx

int _(a) ^(b) f (x) dx =

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

If (2a+2b-x)=f(x), then int_(2a)^(2b)xf(x)dx is equal to