The curve $C\,$ has the parametric equations

\sin t \quad y = 6 \sin 2t \quad 0 \leq t \leq \frac{\pi}{2}

A Cartesian graph with arrowed x- and y-axes, a curve in the first quadrant from the origin to the positive x-axis, and the enclosed region R shaded.

Show that the area of $R\,$ is given by $∫0π248sin⁡tcos⁡2tdt\displaystyle \int_0^{\frac{\pi}{2}} 48 \sin t \cos^2 t dt$

Hence show, by algebraic integration, that the area of $R\,$ is exactly 16

The curve $C\,$ has the parametric equations

\sin t \quad y = 6 \sin 2t \quad 0 \leq t \leq \frac{\pi}{2}

A Cartesian graph with arrowed x- and y-axes, a curve in the first quadrant from the origin to the positive x-axis, and the enclosed region R shaded.

Show that the area of $R\,$ is given by $∫0π248sin⁡tcos⁡2tdt\displaystyle \int_0^{\frac{\pi}{2}} 48 \sin t \cos^2 t dt$

Hence show, by algebraic integration, that the area of $R\,$ is exactly 16

Integration

Integration Questions