`int_0^(4/pi) (3x^2sin(1/x)-xcos(1/x))dx=`
(A) `(8sqrt(2))/pi^3`
(B) `(32sqrt(2))/pi^3`
(C) `(24sqrt(2))/pi^3`
(D) `sqrt(2048)/pi^3`

lim_(xrarr1^(-)) (sqrtpi-sqrt(2sin^-1x))/sqrt(1-x)= (A) sqrt(2/pi) (B) sqrt(pi/2) (C) 1/pi (D) sqrt(1/pi)

int_0^3(3x+1)/(x^2+9)dx = (pi^)/(12)+log(2sqrt(2)) (b) (pi^)/2+log(2sqrt(2)) (c) (pi^)/6+log(2sqrt(2)) (d) (pi^)/3+log(2sqrt(2))

Prove that : int_(0)^(pi//2)(x)/(sin x +cos x)dx= (pi)/(4sqrt(2)) log |(sqrt(2)+1)/(sqrt(2)-1)|

The value of int_(-(pi/4)^(1/3))^((pi/4)^(1/3))(x^2)/((1+sin^2x^3)(1+e^(x^7)))dxi s (a) 1/3tan^(-1)sqrt(2) (b) 1/(3sqrt(2))tan^(-1)sqrt(2) (c) int_0^(pi/4)(sec^2dx)/(sec^2x+tan^2x) (d) 1/3int_0^(pi/4)(sec^2x dx)/(sec^2x+tan^2x)

The integral int_(0)^(pi)sqrt(1+4"sin"^(2)x/2-4"sin"x/2)dx is equals to (a) pi-4 (b) (2pi)/3-4-sqrt(3) (c) (2pi)/3-4-sqrt(3) (d) 4sqrt(3)-4-(pi)/3

A solution of sin^-1 (1) -sin^-1 (sqrt(3)/x^2)- pi/6 =0 is (A) x=-sqrt(2) (B) x=sqrt(2) (C) x=2 (D) x= 1/sqrt(2)

The value of the definite integral int_0^(pi/2)sqrt(tanx)dx is sqrt(2)pi (b) pi/(sqrt(2)) 2sqrt(2)pi (d) pi/(2sqrt(2))

If tan^(-1)x+2cot^(-1)x=(2pi)/3, then x , is equal to (a) (sqrt(3)-1)/(sqrt(3)+1) (b) 3 (c) sqrt(3) (d) sqrt(2)

The value of the definite integral I = int_(0)^(pi)xsqrt(1+|cosx|) dx is equal to (A) 2sqrt(2)pi (B) sqrt(2) pi (C) 2 pi (D) 4 pi

Prove that int_0^(pi/2) \ sin^2 x / (1+sin x cos x) \ dx = pi/(3 sqrt(3)