Question

Use the Midpoint Rule with n = 5 to estimate the volume V obtained by rotating about the y-axis the region under the curve.

Answer 1

\[y=\sqrt{3+9x^2}, 0 \le x \le 1\]

Answer 2

\[\Delta x = \frac{ 1-0 }{ 5 } = 0.2\]
\[V = \int\limits_{0}^{1}2x \pi(\sqrt{3+9x^2)}dx \]
\[=0.4\pi [ f(0.1) + f(0.3) +f(0.5) + f(0.7) + f(0.9)] \]
\[= 0.4\pi[6.567324302] = 8.25\]

My attempt, but the answer is wrong.

Answer 3

\[f(x) = x \sqrt{3+9x^2}\]