Question

find the area enclosed by the curve r²-4cosø

Answer 1

$\displaystyle r^2 = 4\cos{\phi}\\ \begin{aligned} A &= 2 \times \frac{1}{2} \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} 4\cos{\phi} \,\,\mathrm{d}\phi \\&= 4 \sin{\phi}\vert_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \\&= 8 \end{aligned}$