Set up, but do not evaluate, an integral for the area of the surface obtained by rotating the curve $y=\ln x^{7}$ about the x-axis on the interval $1 \leq x \leq 7$ .
A) $\int_{7}^{1} 2 \pi \sqrt{1+\left(\frac{7}{x}\right)^{2}} d x$
B) $\int_{7}^{1} 2 \pi x \ln (x) \sqrt{1+\left(\frac{7}{x}\right)^{2}} d x$
C) $\int_{1}^{7} 2 \pi(7 x) \sqrt{1+\left(\frac{7}{x}\right)^{2}} d x$
D) $\int_{7}^{1} 2 \pi(7 x) \sqrt{1+\left(\frac{7}{x}\right)^{2}} d x$
E) $\int_{1}^{7} 2 \pi(7 \ln (x)) \sqrt{1+\left(\frac{7}{x}\right)^{2}} d x$

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The Answer of Set up, but do not evaluate, an integral for the area of the surface obtained by rotating the curve $y=\ln x^{7}$ about the x-axis on the interval $1 \leq x \leq 7$ .
A) $\int_{7}^{1} 2 \pi \sqrt{1+\left(\frac{7}{x}\right)^{2}} d x$
B) $\int_{7}^{1} 2 \pi x \ln (x) \sqrt{1+\left(\frac{7}{x}\right)^{2}} d x$
C) $\int_{1}^{7} 2 \pi(7 x) \sqrt{1+\left(\frac{7}{x}\right)^{2}} d x$
D) $\int_{7}^{1} 2 \pi(7 x) \sqrt{1+\left(\frac{7}{x}\right)^{2}} d x$
E) $\int_{1}^{7} 2 \pi(7 \ln (x)) \sqrt{1+\left(\frac{7}{x}\right)^{2}} d x$

Set Up, but Do Not Evaluate, an Integral for the Area