Show that the area under the curve y = sin x and y = sin 2x between x = 0 and x = \(\frac { \pi }{ 3 } \) and x axis are as 2:3

Find the volume of the solid generated by the revolution of the loop of the curve x = t² y = t - \(\frac { { t }^{ 3 } }{ 3 } \) about x-axis.

Find the area bounded by the curves y=|x|-1 and y=-|x|+1

Find the area bounded by the curve y2(2a-x)=x² and the line x=2a.

Find the area enclosed by the parabolas 5x²-y=0 and 2x²-y+9=0.