`int_a^(2a)x y` dx where `x^2-y^2=a^2`and `ygeq0`

int_(-a)^(a)x^(2)ydx where x^(2)+y^(2)=a^(2)andyge0

int_(0)^(1)y dx where x=cos2y

int_(0)^(a)y^(2)dx where x=acosthetaandy=bsintheta

int_(0)^((pi)/(2))y^(2)dx where y = sin x

The area common to regions x^2+y^2-2xlt=0 and ygeq sin (pix/2)

The area common to regions x^2+y^2-2xlt=0 and ygeq sin (pix/2)

Write the value of (dy)/dx at (1,0) where x^2y+y^2+x=0 .

int(1)/(3x^(2)y^(2)) where y is constant

Using integration find the area of the region "{"(x , y")":x^2+y^2lt=2a x ,y^2geqa x ,x ,ygeq0} .

If the area bounded by the curve |x+y|+|x-y|=2 is A, then the value of int_(0)^(6A) {x}dx= (where {x}, denotes the fractional part function.