Calculus 3 - Double Integrals

$\begin{align*}&\text{Evaluate the integral, }\iint_{D}(\frac{(6\cdot (\frac{1}{4})^{(x^{2} + y^{2})})}{19}-\frac{ (23e^{(\frac{(2x^{2})}{3}+\frac{ (2y^{2})}{3})})}{3})dA\text{, where D is}\&\text{the region defined between two circles centered on the origin with radii }\&0.27\text{ and }1.18\&\text{and encompassed by vectors from the origin }\&\overrightarrow{u_1}=(-1.000,0.031)\text{ and }\overrightarrow{u_2}=(0.992,-0.125)\&\text{counterclockwise from }\overrightarrow{u_1}\end{align*}$

$\begin{align*}&\text{Evaluate the integral, }\iint_{D}(\frac{(3cos(x^{2} + y^{2}))}{2}-\frac{ cos(2x^{2} + 2y^{2})}{8})dA\text{, where D is}\&\text{the region defined between two circles centered on the origin with radii }\&0.25\text{ and }1.93\&\text{and encompassed by vectors from the origin }\&\overrightarrow{u_1}=(0.218,0.976)\text{ and }\overrightarrow{u_2}=(-0.941,-0.339)\&\text{counterclockwise from }\overrightarrow{u_1}\end{align*}$

Calculate the following Integral.

$\int_{0}^{1}\int_{x}^{x^2} xy^2 dydx$

$\begin{align*}&\text{Evaluate the integral, }\iint_{D}(-\frac{ (13\cdot (\frac{2}{7})^{(2x^{2} + 2y^{2})})}{6}-\frac{ (2\cdot 3^{(\frac{(3x^{2})}{2}+\frac{ (3y^{2})}{2})})}{3})dA\text{, where D is}\&\text{the region defined between two circles centered on the origin with radii }\&0.48\text{ and }0.98\&\text{and encompassed by vectors from the origin }\&\overrightarrow{u_1}=(0.279,0.960)\text{ and }\overrightarrow{u_2}=(-0.982,-0.187)\&\text{counterclockwise from }\overrightarrow{u_1}\end{align*}$

$\begin{align*}&\text{Evaluate the integral, }\iint_{D}(10e^{(x^{2} + y^{2})} +\frac{ (\frac{48}{(\frac{2}{7})^{(\frac{(2x^{2})}{3}+\frac{ (2y^{2})}{3})}})}{5})dA\text{, where D is}\&\text{the region of a circle centered on the origin with a radius of }\&1.16\&\text{and encompassed by vectors from the origin }\&\overrightarrow{u_1}=(0.094,0.996)\text{ and }\overrightarrow{u_2}=(0.941,-0.339)\&\text{counterclockwise from }\overrightarrow{u_1}\end{align*}$

$\begin{align*}&\text{Evaluate the integral, }\iint_{D}(\frac{(\frac{2}{(\frac{7}{2})^{(x^{2} + y^{2})}})}{13}+ 46\cdot (\frac{1}{2})^{(x^{2} + y^{2})})dA\text{, where D is}\&\text{the region of a circle centered on the origin with a radius of }\&1.51\&\text{and encompassed by vectors from the origin }\&\overrightarrow{u_1}=(0.729,0.685)\text{ and }\overrightarrow{u_2}=(0.279,-0.960)\&\text{counterclockwise from }\overrightarrow{u_1}\end{align*}$

$\begin{align*}&\text{Evaluate the integral, }\iint_{D}(\frac{(3cos(2x^{2} + 2y^{2}))}{34}+\frac{ (46sin(\frac{(2x^{2})}{3}+\frac{ (2y^{2})}{3}))}{3})dA\text{, where D is}\&\text{the region of a circle centered on the origin with a radius of }\&0.63\&\text{and encompassed by vectors from the origin }\&\overrightarrow{u_1}=(0.930,0.368)\text{ and }\overrightarrow{u_2}=(-0.536,-0.844)\&\text{counterclockwise from }\overrightarrow{u_1}\end{align*}$

$\begin{align*}&\text{Evaluate the integral, }\iint_{D}(\frac{5}{(x^{2} + y^{2})}+ 2\cdot (\frac{2}{5})^{(x^{2} + y^{2})})dA\text{, where D is}\&\text{the region defined between two circles centered on the origin with radii }\&0.48\text{ and }1.84\&\text{and encompassed by vectors from the origin }\&\overrightarrow{u_1}=(0.891,0.454)\text{ and }\overrightarrow{u_2}=(-0.661,-0.750)\&\text{counterclockwise from }\overrightarrow{u_1}\end{align*}$

$\begin{align*}&\text{Evaluate the integral, }\iint_{D}(\frac{sin(\frac{(2x^{2})}{3}+\frac{ (2y^{2})}{3})}{7}+\frac{ (\frac{5}{4^{(x^{2} + y^{2})}})}{13})dA\text{, where D is}\&\text{the region of a circle centered on the origin with a radius of }\&1.73\&\text{and encompassed by vectors from the origin }\&\overrightarrow{u_1}=(0.368,0.930)\text{ and }\overrightarrow{u_2}=(-0.750,-0.661)\&\text{counterclockwise from }\overrightarrow{u_1}\end{align*}$

Double Integrals

Practice Questions