Find the surface area or volume.
-Use an integral table and a calculator to find to two decimal places the area of the surface generated by revolving the curve $y = x ^ { 2 } , - 1 \leq x \leq 3$, about the $x$-axis.
A) 189.04
B) 265.13
C) 324.07
D) 378.08

Question

Quizplus · Accepted Answer

The surface area generated by revolving the curve $y = x ^ { 2 } , - 1 \leq x \leq 3$ about the x-axis can be calculated using the formula: 
$$
\int_{-1}^{3} 2\pi y \sqrt{1 + \left(\frac{dy}{dx}\right)^2} dx
$$
where $y=x^2$ and $\frac{dy}{dx}=2x$.
Substituting these values and evaluating the integral using a calculator, we get:
$$
\int_{-1}^{3} 2\pi x^2 \sqrt{1 + 4x^2} dx = 265.13
$$
Therefore, the answer is B.

Find the Surface Area or Volume y=x2,−1≤x≤3y = x ^ { 2 } , - 1 \leq x \leq 3y=x2,−1≤x≤3

Find the Surface Area or Volume $y = x ^ { 2 } , - 1 \leq x \leq 3$