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Magazine Problem 86
Use a CAS double-integral evaluator to estimate the values of the integrals. $$\int_{0}^{1} \int_{0}^{1} e^{-\left(x^{2}+y^{2}\right)} d y d x$$
Problem 87
Use a CAS double-integral evaluator to estimate the values of the integrals. $$\int_{0}^{1} \int_{0}^{1} \tan ^{-1} x y d y d x$$
Problem 88
Use a CAS double-integral evaluator to estimate the values of the integrals. $$\int_{-1}^{1} \int_{0}^{\sqrt{1-x^{2}}} 3 \sqrt{1-x^{2}-y^{2}} d y d x$$
Problem 89
Use a CAS double-integral evaluator to find the integrals.$ Then reverse the order of integration and evaluate, again with a CAS. $$\int_{0}^{1} \int_{2 y}^{4} e^{x^{2}} d x d y$$
Problem 90
Use a CAS double-integral evaluator to find the integrals.$ Then reverse the order of integration and evaluate, again with a CAS. $$\int_{0}^{3} \int_{x^{2}}^{9} x \cos \left(y^{2}\right) d y d x$$
Problem 91
Use a CAS double-integral evaluator to find the integrals.$ Then reverse the order of integration and evaluate, again with a CAS. $$\int_{0}^{2} \int_{y^{3}}^{4 \sqrt{2 y}}\left(x^{2} y-x y^{2}\right) d x d y$$
Problem 92
Use a CAS double-integral evaluator to find the integrals.$ Then reverse the order of integration and evaluate, again with a CAS. $$\int_{0}^{2} \int_{0}^{4-y^{2}} e^{x y} d x d y$$
Problem 93
Use a CAS double-integral evaluator to find the integrals.$ Then reverse the order of integration and evaluate, again with a CAS. $$\int_{1}^{2} \int_{0}^{x^{2}} \frac{1}{x+y} d y d x$$
Problem 94
Use a CAS double-integral evaluator to find the integrals.$ Then reverse the order of integration and evaluate, again with a CAS. $$\int_{1}^{2} \int_{y^{3}}^{8} \frac{1}{\sqrt{x^{2}+y^{2}}} d x d y$$
