If f(pi)=2 and int(0)^(pi)(f(x)+f''(x))s...

If `f(pi)=2` and `int_(0)^(pi)(f(x)+f''(x))sin x dx=5`, then `f(0)` is equal to ( it is given that `f(x)` is continuous in `[0,pi]`)

A

7

B

3

C

5

D

1

Verified by Experts

The correct Answer is:

B

Similar Questions

Explore conceptually related problems

If f(pi)=2 and int_(0)^( pi)(f(x)+f'(x))sin xdx=5 then f(0) is equal to

Iff(pi)=2int_0^pi(f(x)+f^(x))sinxdx=5,t h e nf(0) is equal to (it is given that f(x) is continuous in [0,pi])dot 7 (b) 3 (c) 5 (d) 1

If int_(0)^(pi) x f (sin x) dx = A int _(0)^(pi//2) f(sin x) dx , then A is equal to

If f(x) =int_(0)^(x) sin^(4)t dt , then f(x+2pi) is equal to

If int_(0)^(pi)x f(sin x) dx = a int_(0)^(pi)f (sin x) dx , then a =

If f'(x) = f(x)+ int _(0)^(1)f (x) dx and given f (0) =1, then int f (x) dx is equal to :

If f(x)=f(pi+e-x) and int_(e)^( pi)f(x)dx=(2)/(e+pi) then int_(e)^( pi)xf(x)dx is equal to