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shards5
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Homework Statement
Evaluate the integral by reversing the order of integration.
[tex] \int^{3}_{0}\int^{9}_{y^2} y cos(x^2) dydx [/tex]
Homework Equations
...?
The Attempt at a Solution
Drawing the picture out we get a sideways parabola.
From the picture I get the following intervals of integration.
0 [tex]\leq[/tex] y [tex]\leq[/tex] [tex]\sqrt{x}[/tex]
0 [tex]\leq[/tex] x [tex]\leq[/tex] 9
Using the above I get the following integral.
[tex] \int^{9}_{0}\int^{sqrt(x)}_{0} y cos(x^2) dxdy [/tex]
After the first integration I get.
[tex]\frac{y^2}{2}[/tex] cos(x^2)
Plugging in [tex]\sqrt{x}[/tex] and 0 I get the following resulting integral.
[tex] \int^{9}_{0} x/2 * cos(x^2) dy [/tex]
And here is my problem. It has been a while since I took my calculus II so I don't remember how to integrate the above and I am also not sure if I set my intervals of integration correctly.
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