Question 6

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The question

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Let $f(x) = x^2 + 2$ and $g(x) = x^2 - 2x$ , graphed below.

$\text{(a)}$
$R$ is the region between the graphs of $f$ and $g$ from $x = 0$ to $x = 2$ . Write, but do not evaluate, an integral for the area of $R$ .
$\text{(b)}$
$S$ is the region between the graph of $g$ and the $x$ -axis from $x = 2$ to $x = 5$ . $S$ is the base of a solid whose cross sections perpendicular to the $x$ -axis are rectangles with height half their base. Find the volume of the solid. Show the working.
$\text{(c)}$
Write, but do not evaluate, an integral for the volume of the solid formed when $S$ is rotated about the horizontal line $y = 20$ .

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Understanding the Question

This question is about finding area and volume using integrals

Part 1 of 4

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The question

No calculator

Let $f(x) = x^2 + 2$ and $g(x) = x^2 - 2x$ , graphed below.

$\text{(a)}$
$R$ is the region between the graphs of $f$ and $g$ from $x = 0$ to $x = 2$ . Write, but do not evaluate, an integral for the area of $R$ .
$\text{(b)}$
$S$ is the region between the graph of $g$ and the $x$ -axis from $x = 2$ to $x = 5$ . $S$ is the base of a solid whose cross sections perpendicular to the $x$ -axis are rectangles with height half their base. Find the volume of the solid. Show the working.
$\text{(c)}$
Write, but do not evaluate, an integral for the volume of the solid formed when $S$ is rotated about the horizontal line $y = 20$ .

Now playing

This question is about finding area and volume using integrals

Part 1 of 4