Calculus Questions

Test Preparation
1

<p>Hey, I have two Calculus problems that I was hoping someone could check over. They’re easy problems but I don’t know if I’m doing them correctly. Thanks for any help!</p>

<li> Find the area of the region enclosed by the curve y= 2-x2 and the line y= -3x-2. Confirm your answer numerically.<br></li>
</ol>

<p>(I get 1363.538 doing it one way and 20.833 the other. Is either correct? I am assuming that this confirms it numerically.)</p>

<li> The region between the graph of f(x)= 2+cos x and the x-axis over the interval [-2,2] is revolved around the x-axis to generate a solid. Find its volume.</li>
</ol>

<p>(For this one, I’m getting 24.896)</p>

2

<p>20.833 is THE ANSWER</p>

<p>78.213 for pt 2</p>

3

<p>1) solve 2-x^2=-3x-2</p>

<p>x= -1 or 4</p>

<p>integrate [(2-x^2)-(-3x-2)] => -1/3 x^3+ 3/2 x^2 +4x</p>

<p>from -1 to 4 => 125/6 ~ 20.833</p>

<p>--</p>

<ol>
<li>radius is f(x) = 2+cos x</li>
</ol>

<p>integrate Pi * f(x)^2 => Pi[sin(x)cos(x)/2 + 4sin(x) + 9/2x]</p>

<p>from -2 to 2 => ~78.213</p>