If `f(x)=int_0^x e^(cost)/(e^(cost)+e^-(cost))dt`, then `2f(pi)=` (A) `0` (B) `pi` (C) `-pi` (D) none of these

Let f(x)=int_0^x (sin^100t)/(sin^100t+cos^100t)dt then f(2pi)= (A) 2f(pi/2) (B) 4f(pi/2) (C) f(pi/2) (D) none of these

If f(x)=int_0^sinx cos^-1t dt+int_0^cosx sin^-1t dt, 0ltxltpi/2 , then f(pi/4)= (A) 0 (B) pi/sqrt(2) (C) 1 (D) none of these

If f(x)=int_0^sinx cos^-1t dt+int_0^cosx sin^-1t dt, 0ltxltpi/2 , then f(pi/4)= (A) 0 (B) pi/sqrt(2) (C) 1 (D) pi/(2sqrt(2))

If f(x) = int_(0)^(x^(2)) sqrt(cost)dt , find f'(x)

If f(x) = int_(0)^(x^(2)) sqrt(cost)dt , find f'(x)

If f(x)=int_0^x("cos"(sint)+"cos"(cost)dt , then f(x+pi) is (a) f(x)+f(pi) (b) f(x)+2(pi) (c) f(x)+f(pi/2) (d) f(x)+2f(pi/2)

The value of int_0^(log5) (e^xsqrt(e^x-1))/(e^x+3)dx is (A) 3+2pi (B) 4-pi (C) 2+pi (D) none of these

Let F(x)=int_(0)^(x)(cost)/((1+t^(2)))dt,0lex le2pi . Then -

If f(x)=int_0^x("cos"(sint)+"cos"(cost)dt ,t h e nf(x+pi)i s (a) f(x)+f(pi) (b) f(x)+2(pi) (c) f(x)+f(pi/2) (d) f(x)+2f(pi/2)

If f(x)=int_0^x("cos"(sint)+"cos"(cost)dt ,t h e nf(x+pi)i s (a) f(x)+f(pi) (b) f(x)+2(pi) (c) f(x)+f(pi/2) (d) f(x)+2f(pi/2)