INTEGRATION OF FUNCTION F(G(X))G'(X)

Let a function f be even and integrable everywhere and periodic with period 2. Let g(x)=int_0^x f(t) dt and g(t)=k The value of g(x+2)-g(x) is equal to (A) g(1) (B) 0 (C) g(2) (D) g(3)

Let a function f be even and integrable everywhere and periodic with period 2. Let g(x)=int_0^x f(t) dt and g(t)=k The value of g(x+2)-g(x) is equal to (A) g(1) (B) 0 (C) g(2) (D) g(3)

f and g differentiable functions of x such that f(g(x))=x," If "g'(a)ne0" and "g(a)=b," then "f'(b)=

If f(x) be a function such that f(-x)= -f(x),g(x) be a function such that g(-x)= -g(x) and h(x) be a function such that h(-x)=h(x) , then choose the correct statement: I. h(f(g(-x)))=-h(f(g(x))) II. f(g(h(-x)))=f(g(h(x))) III. g(f(-x))=g(f(x))

Let g be the greatest integer function. Then the function f(x)=(g(x))^(2)-g(x) is discontinuous at

Method of integration by parts : int[f(x)g''(x)-f''(x)g(x)]dx=....

Evaluation of definite integrals by subsitiution and properties of its : f is a function such that f'(x)=f(x) and f(0)=1g(x) is a function such that g(x)+f(x)=x^(2) then int_(0)^(1)f(x)g(x)dx=………

Let f:R rarr R and g:R rarr R be continuous functions.Then the value of the integral int_((pi)/(2))^((pi)/(2))[f(x)+f(-x)][g(x)-g(-x)]dx is