Chapter 7.4, Problem 14P

Use the results of Problem 13 to evaluate the following integrals without calculation.

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(a) ${\displaystyle {\int }_0^{4\pi /3}{\sin }^2}\left(\frac{3x}{2}\right)dx$

(b) ${\displaystyle {\int }_{-\pi /2}^{3\pi /2}{\cos }^2}\left(\frac{x}{2}\right)dx$