QuestionWhante $\int_{D} 2 d A$, where $D=\{(x, y): 0 \leq x \leq 1, x \leq y \leq 1+x)$. $A .0$ B. 3 0.4
3. Folluate $\iint_{D} 10 d A$, where $D=\{(x, y): 0 \leq y \leq 2,0 \leq x \leq y\}$. A. 1 B. 5 C. 10 D. 20
14. If $f(x, y)=4$, evaluate $\iint_{R} f(x, y) d A$, where $R=\{(r, \theta): 1 \leq r \leq 2,0 \leq \theta \leq \pi\}$. A. $\pi$ B. $3 \pi$ C. $6 \pi$ D. $10 \pi$
15. Express $\int_{-a}^{a} \int_{0}^{\sqrt{a^{2}-x^{2}}}\left(x^{2}+y^{2}\right)^{3 / 2} d y d x$ in polar coordinates. A. $\int_{0}^{\pi / 2} \int_{0}^{a} r^{5} d r d \theta$ B. $\int_{0}^{\pi} \int_{0}^{a} r^{4} d r d \theta$ C. $\int_{0}^{\pi} \int_{0}^{a} r^{3} d r d \theta$ D. $\int_{0}^{\pi} \int_{0}^{2 \cos \theta} r^{2} d r d \theta$
16. Express $\iiint_{E} x z^{3} d V$, where $E=\left\{(x, y, z): 0 \leq x \leq 1,0 \leq y \leq x, 0 \leq z \leq x^{2} y^{2}\right\}$ in a form that can be evaluated. A. $\int_{0}^{x^{2} y^{2}} \int_{0}^{x} \int_{0}^{1} x z^{3} d x d y d z$ B. $\int_{0}^{x} \int_{0}^{1} \int_{0}^{x^{2} y^{2}} x z^{2} d z d x d y$ C. $\int_{0}^{1} \int_{0}^{x^{2} y^{2}} \int_{0}^{x} x z^{2} d y d z d x$ D). $\int_{0}^{1} \int_{0}^{x} \int_{0}^{x^{2} y^{2}} x z^{2} d z d y d x$
17. | et $E=\left\{(r, 0, z): 0 \leq 0 \leq \pi, 0 \leq r \leq 2,1 \leq z \leq r^{2}\right\}$ and $f(x, y, z)=2$. lixpress $\iiint_{E} f(x, y, z) d V$ in cylindrical condinates. ค. $\int_{0}^{\pi} \int_{0}^{2} \int_{1}^{r^{2}} z r d \% d r d 0$
13. $\int_{0}^{11} \int_{0}^{2} \int_{1}^{r^{2}} \% d \% d r d()$ (i. $\int_{0}^{3 x} \int_{0}^{2} \int_{1}^{r^{2}} z r^{2} d z d r d 0$ 1) $\int_{1}^{11} \int_{11}^{2} \int_{1}^{r^{2}} z r d \% d 0 d r$
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