9. Graphical Applications of Integrals

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 $\textcolor{blue}{f\left(x\right)=-\left(x-2\right)^2+5}$ & $\textcolor{orange}{g\left(x\right)=4x}$ on the interval $\left\lbrack0,1\right\rbrack$. Then set up an integral to represent the region's area and evaluate.

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

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 shown in the first quadrant between $f\left(x\right)=\frac{1}{x}$ & $g\left(x\right)=-\frac{1}{4}x+\frac{5}{4}.$

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

Find the area of the shaded region between $f\left(x\right)=\frac{1}{x}$ & $g\left(x\right)=x$ from $x=0.5$ to $x=4$.