How do you integrate $\int cos (\frac{2 x}{3})$ $int cos((2x)/3)$ from [0, pi/2]?

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How do you integrate $\int cos (\frac{2 x}{3})$ $int cos((2x)/3)$ from [0, pi/2]?

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Answer 1 · 2017-02-13T22:27:00

$\int_{0}^{\frac{π}{2}} cos (\frac{2 x}{3}) d x = \frac{3}{2} \int_{0}^{\frac{π}{2}} cos (\frac{2 x}{3}) d (\frac{2 x}{3}) = \frac{3}{2} {[sin (\frac{2 x}{3})]}_{0}^{\frac{π}{2}} = \frac{3}{2} (sin (\frac{π}{3}) - sin 0) = \frac{3 \sqrt{3}}{4}$ $int_0^(pi/2) cos((2x)/3)dx = 3/2 int_0^(pi/2) cos((2x)/3)d((2x)/3) = 3/2 [sin((2x)/3)]_0^(pi/2) = 3/2( sin (pi/3) -sin 0) = (3sqrt(3))/4$

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How do you integrate $\int cos (\frac{2 x}{3})$ $int cos((2x)/3)$ from [0, pi/2]?

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