Let `f(x)=int_1^xsqrt(2-t^2)dtdot` Then the real roots of the equation `x^2-f^(prime)(x)=0` are (a)`+-1` (b) `+-1/(sqrt(2))` (c)`+-1/2` (d) 0 and 1

The sum of real roots of the equation |x-2|^2+|x-2|-2=0 is (A) 4 (B) 1 (C) 2 (D) -2

Let f(x)=int_(1)^(x)(3^(t))/(1+t^(2))dt , where xgt0 , Then

Let f(x)=1/x^2 int_0^x (4t^2-2f'(t))dt then find f'(4)

If a

Let f(x)=int x^2/((1+x^2)(1+sqrt(1+x^2)))dx and f(0)=0 then f(1) is

Let: f(x)=int_0^x|2t-3|dtdot Then discuss continuity and differentiability of f(x)a tx=3/2

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

Let f(x)=inte^x(x-1)(x-2)dxdot Then f decreases in the interval (a) (-oo,-2) (b) -2,-1) (c) (1,2) (d) (2,+oo)

The sum of the solution of the equation 2sin^(-1)sqrt(x^2+x+1)+cos^(-1)sqrt(x^2+x)=(3pi)/2 is (a)0 (b) -1 (c) 1 (d) 2

Let f be a real-valued function defined on the inverval (-1,1) such that e^(-x)f(x)=2+int_0^xsqrt(t^4+1)dt , for all, x in (-1,1)a n dl e tf^(-1) be the inverse function of fdot Then (f^(-1))^'(2) is equal to 1 (b) 1/3 (c) 1/2 (d) 1/e