Question

-/1.81 points details my notes ask your teacher sketch the region enclosed by the given curves. decide whether to integrate with respect to x or y. draw a typical approximating rectangle. (y = \frac{4}{x},y=\frac{4}{x^{2}},x = 7) find the area of the region.

Explanation:

Step1: Find intersection of curves

Set $\frac{4}{x}=\frac{4}{x^{2}}$, solve for $x$ ($x = 1$).

Step2: Set up integral

Integrate with respect to $x$: $\int_{1}^{7}(\frac{4}{x}-\frac{4}{x^{2}})dx$.

Step3: Evaluate integral

$4\ln x+\frac{4}{x}\big|_{1}^{7}=4\ln7+\frac{4}{7}-4$.

Answer:

$4\ln7+\frac{4}{7}-4$