9. Graphical Applications of Integrals

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.

Calculate the area of the shaded region between the 2 functions from $x=0$ to $x=9$

Calculate the area of the shaded region between $f\left(x\right)$ & $g\left(x\right)$ contained between $x=-4$ & $x=-2$.

Sketch the region bounded by $f\left(x\right)=-{(x-2)}^2+5$ & $g\left(x\right)=4x$ on the interval $[0,1]$. Then set up an integral to represent the region's area and evaluate.

Find the area between $f\left(x\right)=x^2-4$ & $g\left(x\right)=-x^2+4$.

Find the area of the shaded region between $f\left(x\right)=x^4-x^2$ & $g\left(x\right)=3x^2$.

Find the area of the shaded region ONLY that lies between the line $y=1$ & $f\left(x\right)=\sin 2x$.

Find the shaded area between $f\left(x\right)=x^3+2x^2$ & $g\left(x\right)=x+2$.

Find the area of the shaded region between $f\left(x\right)=\sin 2x$ & $g\left(x\right)=2\sin x$ from $x=0$ to $x=2\pi$.