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

If f(x)=int_(0)^(x)(sin^(4)t+cos^(4)t)dt, then f(x+pi) will be equal to

On which of the following intervals is the function f given by f(x)=x^(100)+sinx-1 strictly decreasing ? (A) (0, 1) (B) (pi/2,pi) (C) (0,pi/2) (D) None of these

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

Off(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^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)}^(101)=int_(0)^(x)(F(t))^(100)(dt)/(1+sin t), then find F(x)

If f(x)=sin^(-1)cos x, then the value of f(10)+f'(10) is (a)11-(7 pi)/(2) (b) (7 pi)/(2)-11 (c) (5 pi)/(2)-11( d) none of these

If f(x)=sin x+int_(0)^((pi)/(2))sin x cos tf(t)dt, then int_(0)^((pi)/(2))f(x)dx=