I have though about u-subbing or just looking for similarities between the two integrals but those approaches seem to be getting me nowhere. I don't think I've seen a problem like this before, I am stumped. Help?
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1What $u$-sub did you try and show your work for your attempt. – Eric Towers Sep 19 '20 at 18:02
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Well first off can you tell that both integrals will be positive? (That eliminates some possibles) Then there is in fact an obvious substitution to try. – Mark Bennet Sep 19 '20 at 18:03
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If we take $u=4-x^2 \Rightarrow du = -2x dx$ and if $x=1 \Rightarrow u=3,\, x=2 \Rightarrow u=0.$ Then
$$\int_1^2 xe^{\sin(4-x^2)}dx = \int_3^0-\frac{e^{\sin u}}{2}du = \int_0^3\frac{e^{\sin u}}{2}du = \frac{k}{2}$$
Alex Pozo
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