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![Q4 [15]
Evaluate \( \int e^{3 x} \sin (2 x) d x \)](https://media.cheggcdn.com/media/416/416d4238-8676-40c4-842a-f3d1f2cfacf6/phpEVemBs)
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(a) Evaluate \( \int_{0}^{\frac{\pi}{4}} \sin ^{7}(2 x) \cos (2 x) d x \).](https://media.cheggcdn.com/media/780/7803fc45-3d46-445e-88d7-30dac8bc707f/phplD5Zpu)
Expert Answer
Sol-4.To evaluate: the value of the integral ?Reorder and . Integrate by parts using the formula , where and . Since is constant with respect to , move out of the integral. Combine fractions. Integrate by parts using the formula , where and . Since is constant with respect to , move out of the integral. Simplify terms. Solving for , we find that = . Simplify the answer.