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<title>
12.2 - Double integrals practice
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<h2>
[12.2] - Double Integrals - Practice
</h2>
<ol>
<li>$\int_0^2\int_0^2(x^2-y^2)\,dy\,dx$
<br><br><br><br><br><br>

<li>$\int_0^{\frac{\pi}{4}}\int_{y=0}^{\frac{\pi}{2}}\cos(2x+y)\,dy\,dx$
<br>Hint: According to one of the <a href="http://mathworld.wolfram.com/TrigonometricAdditionFormulas.html">Trig addition formulas</a>, $\cos(\alpha+\beta)=
\cos(\alpha)\cos(\beta)  - \sin(\alpha)\sin(\beta)$
<br><br><br><br><br><br>

<li>$\int_0^2\int_{y=1}^3x^3y\,dy\,dx$
<br><br><br><br><br><br>

<li>$\int_{-1}^{1}\int_{y=0}^{\pi}x^2\sin y\,dy\,dx$
<br><br><br><br><br><br>

<li>$\int_0^2\int_{y=x^2}^{2x}(x^2+2y)\,dy\,dx$
<br><br><br><br><br><br>

<li>$\int_0^3\int_{y=0}^{9-x^2}4x\,dy\,dx$
<br><br>


</ol>
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<p class="answer">Answers: 1.) 0 &nbsp; &nbsp; 2.) 0 &nbsp; &nbsp; 
3.) 16 &nbsp; &nbsp; 
4.) $\frac 43$ &nbsp; &nbsp; 
5.) $\frac{88}{15}$ &nbsp; &nbsp; 
6.) 81

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