Calculus 3 - Multiple Integration

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

$\begin{align*}&\text{Evaluate the triple integral}\int_{3}^{5.5}\int_{4}^{5}\int_{-6}^{-1.5}(\frac{(3\cdot 3^{(\frac{z}{2})}\cdot 3^y)}{(74x^{2})})dxdydz\end{align*}$

$\begin{align*}&\text{Evaluate the triple integral}\int_{2}^{5}\int_{-6}^{-1}\int_{9}^{14}(\frac{(sin(3y)e^{(4x)})}{(6z)})dxdydz\end{align*}$

$\begin{align*}&\text{Evaluate the triple integral}\int_{-9}^{-6}\int_{4}^{5}\int_{10}^{11}(\frac{(6xe^{(-z)})}{(31y)})dxdydz\end{align*}$

Evaluate the following integral by converting into Polar Coordinates.

$\int \int_D 10xy \ dA$ , where is the portion between the circles of radius and and lies in first quadrant.

$\begin{align*}&\text{Evaluate the triple integral}\int_{10}^{11.5}\int_{-3.5}^{1.5}\int_{9}^{13.5}(25sin(3x)sin(4z)e^{(2y)})dxdydz\end{align*}$

$\begin{align*}&\text{Evaluate the integral, }\iint_{D}(-10cos(z + 1)sin(2x^{2} + 2y^{2}))dA\text{, where D is}\&\text{the region of a cylinder centered on the origin with a radius of }\&1.22\&\text{and length }1.91\&\text{and encompassed by vectors from the origin }\&\overrightarrow{u_1}=(-0.536,0.844)\text{ and }\overrightarrow{u_2}=(0.637,-0.771)\&\text{counterclockwise from }\overrightarrow{u_1}\end{align*}$

$\begin{align*}&\text{Evaluate the integral, }\iint_{D}(11cos(\frac{(3x^{2})}{2}+\frac{ (3y^{2})}{2})sin(3z))dA\text{, where D is}\&\text{the region of a cylinder centered on the origin with a radius of }\&1.31\&\text{and length }0.65\&\text{and encompassed by vectors from the origin }\&\overrightarrow{u_1}=(1.000,0.031)\text{ and }\overrightarrow{u_2}=(-0.976,-0.218)\&\text{counterclockwise from }\overrightarrow{u_1}\end{align*}$

$\begin{align*}&\text{Evaluate the triple integral}\int_{10}^{11.5}\int_{-3.5}^{1.5}\int_{9}^{13.5}(25sin(3x)sin(4z)e^{(2y)})dxdydz\end{align*}$

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

Multiple Integration

Practice Questions