Evaluate `intsqrt (2+sin3t) cos3t dt`

Evaluate: intsqrt (sin2x)cos2xdx

Evaluate: intsqrt(t a ntheta)\ d theta

Evaluate the following integral: int_0^(pi//4)sin^3 2tcos2t\ dt

Find the equation of tangent to the curve given by x=2 sin^(3)t ,y=2 cos^(3)t at a point where t=(pi)/(2) ?

int(4+sqrt(t))/(t^(3))dt

Find the equation of the tangent to the curve x=sin3t ,y=cos2t at t=pi/4dot

Show that the equation of normal at any point t on the curve x=3 cos t - cos^(3) t and y=3 sin t - sin^(3) t is 4(y cos^(3) t-x sin^(3) t) = 3 sin 4t .

If x and y are connected parametrically by the equations given, without eliminating the parameter, Find (dy)/(dx) . x=(sin^3t)/(sqrt(cos2t)), y=(cos^3t)/(sqrt(cos2t))

Find the equations of the tangent and the normal at the point ' t ' on the curve x=a\ sin^3t , y=b\ cos^3t .

If x=a (cos t + t sin t) and y=a ( sin t- t cos t), find (d^(2)y)/(dx^(2))