If `int_0^x(f(t))dt=x+int_x^1(t^2.f(t))dt+pi/4-1`, then the value of the integral `int_-1^1(f(x))dx` is equal to

If int_(0)^(x) f(t)dt=x+int_(x)^(1) t f(t) dt , then the value of f(1), is

If int_(0)^(x)f(t)dt=x+int_(x)^(1)f(t)dt ,then the value of f(1) is

If f(x)=x+int_(0)^(1)t(x+t)f(t)dt, then find the value of the definite integral int_(0)^(1)f(x)dx

f(x)=int_(0)^( pi)f(t)dt=x+int_(x)^(1)tf(t)dt, then the value of f(1) is (1)/(2)

If int_(0) ^(x) f (t) dt = x + int _(x ) ^(1) t f (t) dt, then the value of f (1) , is

If int_(0)^(1) f(t)dt=x^2+int_(0)^(1) t^2f(t)dt , then f'(1/2)is

Let f(x) is a continuous function If f(1)=1 and int_(0)^(x)t.f(2x-t)dt=(1)/(2)tan^(-1)(x^(2)) then the value of a? 4int_(1)^(2)f(x)dx is equal to

If int_(0)^(x^(2)(1+x))f(t)dt=x , then the value of f(2) is.

If int_(0)^(x)f(t)dt=x^(2)+int_(x)^(1)t^(2)f(t)dt, then f'((1)/(2)) is