9. Graphical Applications of Integrals

Which of the following integrals correctly represents the area of the region enclosed by the curves $y=x^2$ and $y=2x$ for $x\in [0,2]$?

Find the area enclosed by one loop of the curve $r=\sin \left(6\theta \right)$.

Determine the area of the shaded region in the following figures.

Given the parametric equations $x=t^2-2t$ and $y=t$ for $t\in [0,2]$, what is the area enclosed by the curve and the y-axis?

Shade the region bounded by $f\left(x\right)=\sin x$ & $g\left(x\right)=\cos 2x$ on the interval $[\frac{\pi }{6},\frac{5\pi }{6}]$. Then set up an integral to represent the region's area.

Which of the following integrals correctly represents the area of the region enclosed by the curves $y=2x$, $y=8x$, and $y=18x$ for $x>0$?

Find the area of the region bounded by the curves $y=6x^2\ln \left(x\right)$ and $y=24\ln \left(x\right)$ for $x>0$.