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Evaluate the double integral.
$$\iint_{D} x \cos y d A, \quad \Delta$$ is bounded by $$y=$$ 0, $$y=x^{2}, x=\frac{\pi}{2}$$

$$\iint_{R} x \cos y d A$$

$$\int_{0}^{x^{2}} \int_{0}^{\frac{\pi}{2}} x \cos y d x d y=\int_{0}^{\frac{\pi}{2}} \left (\int_{0}^{x^{2}} \cos y d y\right) d x$$

$$=\int_{0}^{\pi/2}x|_{0}^{\pi/2} \sin y d x=\int_{0}^{\frac{\pi}{2}} x\left[\sin x^{2}-\sin 0\right] d x$$

$$=\int_{0}^{\pi/2} \frac{1}{2}(2 x)\left[\sin x^{2}\right] d x=|_{0}^{\pi/2}-\frac{1}{2} \cos x^{2} $$

$$\int_{R} \int (\cos y) x=\frac{1}{2}\left[\cos (0)^{2}-\cos \left(\frac{\pi}{2}\right)^2\right]=0.89$$

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