Problem

An artist friend observes that the bodies in Figu…

Problem 3 Easy Difficulty

a. Write an integral that is the volume of the body with base the region of the $x, y-$ plane bounded by
$$
y_{1}=0.25 \sqrt{x} \sqrt[4]{2-x} \quad y_{2}=-0.25 \sqrt{x} \sqrt[4]{2-x} \quad 0 \leq x \leq 2
$$
and with each cross section perpendicular to the $x$ -axis at $x$ being a square with lower edge having endpoints $\left[x, y_{2}(x), 0\right]$ and $\left[x, y_{1}(x), 0\right]$ (see Exercise Figure 11.1.5A). (The value of the integral is $4 \sqrt{2} / 15$ ).
b. Write an integral that is the volume of the body with base the region of the $\mathrm{x}, \mathrm{y}$ -plane bounded by
$$
y_{1}=0.25 \sqrt{x} \sqrt[4]{2-x} \quad y_{2}=-0.25 \sqrt{x} \sqrt[4]{2-x} \quad 0 \leq x \leq 2
$$
and with each cross section perpendicular to the $x$ -axis at $x$ being an equilateral triangle with lower edge having endpoints $\left[x, y_{2}(x), 0\right]$ and $\left[x, y_{1}(x), 0\right]$ (see Exercise Figure $11.1 .5 \mathrm{~B}$ ). (The value of the integral is $\sqrt{6} / 15$ ).

Answer

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Calculus 2 / BC

Calculus for the Life Sciences: A Modeling Approach Volume I

Chapter 11

Applications of the Fundamental Theorem

Section 1

Volume

Related Topics

Applications of Integration

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Video Transcript

that's draw the region first. These curve is why equal to square roots off three minus sets and the wrath line is X equal to chew, since the shape off a cross section off the given solid is square with the inside while like these screen blinds in part a, the area a off X is Y squared, which is three minus x in part B. Here is the formula off volume according to general slicing method things that is protein between 0 to 2 and a affects is three minus X. So the volume is IT girl from 0 to 23 minus x the X uh

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Calculus for the Life Sciences: A Modeling Approach Volume I

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