If `f(x)` is a function satisfying `f(1/x)+x^2f(x)=0` for all nonzero `x` , then evaluate `int_(sintheta)^(cos e ctheta)f(x)dx`

If f(x) is a function satisfying f(1/x)+x^(2)f(x)=0 for all non zero x then int_(cos theta)^(sec theta)f(x)dx=

If f(x) is a function satisfying f(x+a)+f(x)=0 for all x in R and positive constant a such that int_(b)^(c+b)f(x)dx is independent of b, then find the least positive value of c.

If f(x) is a continuous function satisfying f(x)=f(2-x) , then the value of the integral I=int_(-3)^(3)f(1+x)ln ((2+x)/(2-x))dx is equal to

If a function f(x) satisfies f'(x)=g(x) . Then, the value of int_(a)^(b)f(x)g(x)dx is

If f(x) and g(x) are continuous functions satisfying f(x) = f(a-x) and g(x) + g(a-x) = 2 , then what is int_(0)^(a) f(x) g(x)dx equal to ?

Let f(x) be a continuous function such that f(a-x)+f(x)=0 for all x in [0,a] . Then, the value of the integral int_(0)^(a) (1)/(1+e^(f(x)))dx is equal to

If f is an odd function,then evaluate I=int_(-a)^(a)(f(sin x))/(f(cos x)+f(sin^(2)x))dx