1) Evaluate \( \int_{0}^{a} \int_{x}^{a}\left(x^{2}+y^{2}\right) d y d x \) and plot the region of integration. 2) Evaluate the

1) Evaluate \( \int_{0}^{a} \int_{x}^{a}\left(x^{2}+y^{2}\right) d y d x \) and plot the region of integration. 2) Evaluate the double integral \( \iint x y d x d y \) taken over the positive quadrant of the ellipse \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \)

1) Evaluate \( \int_{0}^{a} \int_{x}^{a}\left(x^{2}+y^{2}\right) d y d x \) and plot the region of integration. 2) Evaluate the double integral \( \iint x y d x d y \) taken over the positive quadrant of the ellipse \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \)

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