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Let
kappa be the region enclosed by the
y-axis, the line
y=4 and the curve
y=x^(2).
A solid is generated by rotating
R about the line
y=4.
What is the volume of the solid?

Let $\kappa$ be the region enclosed by the $y$ -axis, the line $y=4$ and the curve $y=x^{2}$ . $\newline$ A solid is generated by rotating $R$ about the line $y=4$ . $\newline$ What is the volume of the solid?

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Write a linear equation from a slope and y-intercept

Full solution

Q. Let

\kappa

be the region enclosed by the

y

-axis, the line

y=4

and the curve

y=x^{2}

.

\newline

A solid is generated by rotating

R

about the line

y=4

.

\newline

What is the volume of the solid?

Identify method: Identify the method to find the volume of the solid generated by rotation.
Set up integral: Set up the integral for the volume using the disk method.
Calculate volume: Calculate the integral to find the volume.
Expand and simplify: Expand the integrand and simplify.
Integrate terms: Integrate term by term.
Evaluate at bounds: Evaluate the integral at the bounds.

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