next hw is ready

multipleIntegrals/exercisesMoreNontrivialRegions/exerciseList.tex

@@ -0,0 +1,10 @@
+\documentclass{xourse}
+
+\input{../../preamble.tex}
+
+\begin{document}
+\part{More integrals with trivial integrands}
+\practice{volume1.tex}
+\practice{volume2.tex}
+\practice{setup3D1.tex}
+\end{document}

multipleIntegrals/exercisesNontrivialRegions/apex13-2-10.tex

@@ -0,0 +1,30 @@
+\documentclass{ximera}
+
+\input{../../preamble.tex}
+\author{Gregory Hartman \and Bart Snapp}
+\license{Creative Commons 3.0 By-NC}
+\acknowledgement{https://github.com/APEXCalculus}
+
+\outcome{Use iterated integrals to compute multiple integrals.}
+\outcome{Apply Fubini's Theorem.}
+
+\begin{document}
+\begin{exercise}
+  Compute:
+  \[
+  \int_0^{9}\int_{y/3}^{\sqrt{y}} \d x \d y
+  \begin{prompt}
+    = \answer{9/2}
+  \end{prompt}
+  \]
+  \begin{exercise}
+    Now set-up an integral that computes the area of the same region
+    where one integrates with respect to $y$ and then with respect to $x$.
+    \begin{prompt}
+      \[
+      \int_{\answer{0}}^{\answer{3}} \int_{\answer{x^2}}^{\answer{3x}} \d y \d x
+      \]
+    \end{prompt}
+  \end{exercise}
+\end{exercise}
+\end{document}

multipleIntegrals/exercisesNontrivialRegions/apex13-2-21.tex

@@ -0,0 +1,24 @@
+\documentclass{ximera}
+
+\input{../../preamble.tex}
+\author{Gregory Hartman \and Bart Snapp}
+\license{Creative Commons 3.0 By-NC}
+\acknowledgement{https://github.com/APEXCalculus}
+
+\outcome{Use iterated integrals to compute multiple integrals.}
+\outcome{Apply Fubini's Theorem.}
+
+\begin{document}
+\begin{exercise}
+  Compute:
+  \[
+  \int_0^{1}\int_{y}^{1}  \frac{2y}{x^2+y^2}\d x \d y
+  \begin{prompt}
+    = \answer{\ln(2)}
+  \end{prompt}
+  \]
+  \begin{hint}
+    Change the order of integration.
+  \end{hint}
+\end{exercise}
+\end{document}

multipleIntegrals/exercisesNontrivialRegions/apex13-2-9.tex

@@ -0,0 +1,30 @@
+\documentclass{ximera}
+
+\input{../../preamble.tex}
+\author{Gregory Hartman \and Bart Snapp}
+\license{Creative Commons 3.0 By-NC}
+\acknowledgement{https://github.com/APEXCalculus}
+
+\outcome{Use iterated integrals to compute multiple integrals.}
+\outcome{Apply Fubini's Theorem.}
+
+\begin{document}
+\begin{exercise}
+  Compute:
+  \[
+  \int_0^{1}\int_{-\sqrt{1-y}}^{\sqrt{1-y}} \d x \d y
+  \begin{prompt}
+    = \answer{4/3}
+  \end{prompt}
+  \]
+  \begin{exercise}
+    Now set-up an integral that computes the area of the same region
+    where one integrates with respect to $y$ and then with respect to $x$.
+    \begin{prompt}
+      \[
+      \int_{\answer{-1}}^{\answer{1}} \int_{\answer{0}}^{\answer{1-x^2}} \d y \d x
+      \]
+    \end{prompt}
+  \end{exercise}
+\end{exercise}
+\end{document}

multipleIntegrals/exercisesNontrivialRegions/exerciseList.tex

@@ -6,11 +6,12 @@
 \part{Integrals with trivial integrands}
 \practice{area1.tex}
 \practice{area2.tex}
-\practice{volume1.tex}
-\practice{volume2.tex}
 \practice{setup2D0.tex}
 \practice{setup2D1.tex}
 \practice{setup2D2.tex}
+\practice{apex13-2-9.tex}
+\practice{apex13-2-10.tex}
 \practice{impossible1.tex}
-\practice{setup3D1.tex}
+\practice{apex13-2-21.tex}
+\practice{impossible2.tex}
 \end{document}

multipleIntegrals/exercisesNontrivialRegions/impossible2.tex

@@ -0,0 +1,23 @@
+\documentclass{ximera}
+
+\input{../../preamble.tex}
+
+\author{Bart Snapp}
+
+\outcome{Use iterated integrals to compute multiple integrals.}
+\outcome{Apply Fubini's Theorem.}
+
+\begin{document}
+\begin{exercise}
+  Compute:
+  \[
+  \int_0^{\infty}\int_y^{\infty} e^{-x^2/2}\d x \d y
+  \begin{prompt}
+    = \answer{1}
+  \end{prompt}
+  \]
+  \begin{hint}
+    Change the order of integration.
+  \end{hint}
+\end{exercise}
+\end{document}