If `cosxdy/dx-y sin x=6x, (0ltxltx/2)and y(pi/3)=0`, then `y(pi/6)` is equal to (a) `pi^(2) /(2sqrt 3)` (b) `-pi^(2) /(2sqrt 3)` (c) `-pi^(2) /(4sqrt 3)` (d) (c) `-pi^(2) /2`

If y(x) satisfies the differential equation cosx (dy)/(dx)-y sinx =6x . And y((pi)/(3))=0 . Then value of y((pi)/(6)) is (A) (pi^(2))/(2sqrt(3)) (B) -(pi^(2))/2 (C) -(pi^(2))/(2sqrt(3)) (D) -(pi^(2))/(4sqrt(3))

If (dy)/(dx) +y sec x=tan x," then (sqrt(2) +1) y((pi)/(4)) - y(0)=, (A) sqrt(2) - (pi)/(4) (B) sqrt(2) + (pi)/(4) (C) sqrt(2) - (pi)/(2) (D) sqrt(2) + (pi)/(2)

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))

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

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

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

If sin^(-1)x+sin^(-1)y=(pi)/(2) and sin2x=cos2y, then (a)x=(pi)/(8)+sqrt((1)/(2)-(pi^(2))/(64))(b)y=sqrt((1)/(2)-(pi^(2))/(64))-(pi)/(12)(c)x=(pi)/(12)+sqrt((1)/(2)-(pi^(2))/(64))(d)y=sqrt((1)/(2)-(pi^(2))/(64))-(pi)/(8)

tan^(-1)sqrt(3)-cot^(-1)(-sqrt(3)) is equal to (A) pi (B) -pi/2 (C) 0 (D) 2sqrt(3)

int_((5)/(2))^(5)(sqrt((25-x^(2))^(3)))/(x^(4))dx is equal to (a) (pi)/(6)(b)(2 pi)/(3)(5 pi)/(6) (d) (pi)/(3)