Answer to Question #290600 in Calculus for Denz

Question

Sketch the region enclosed by the curves and find its area.

y=e^x, y=e^8x, x=0, x=ln2

Answer 1

$$e^x=e^{8x}=>x=0$$

$$A=\displaystyle\int_{0}^{\ln 2}(e^{8x}-e^x)dx=[\dfrac{e^{8x}}{8}-e^x]\begin{matrix} \ln 2 \\ 0 \end{matrix}$$

$$=\dfrac{256}{8}-2-(\dfrac{1}{8}-1)$$

$$=\dfrac{247}{8}({units}^2)=30.875{units}^2$$