Use a symbolic integration utility to evaluate the double integral. $\int _ { 1 } ^ { 2 } \int _ { 0 } ^ { x } e ^ { x y } d y d x$
A)8.1747
B)9.1211
C)6.2031
D)7.88.7522
E)9.4362

Question

Quizplus · Accepted Answer

The correct answer is obtained by first integrating $e^{xy}$ with respect to $y$ from 0 to $x$, and then integrating the result with respect to $x$ from 1 to 2. The integration process involves finding the antiderivative of $e^{xy}$ with respect to $y$, which is $\frac{e^{xy}}{x}$, and then evaluating this from 0 to $x$, resulting in $\frac{e^{x^2}}{x} - \frac{1}{x}$. Integrating this expression from 1 to 2 with respect to $x$ yields the numerical result of approximately 8.1747.

Use a Symbolic Integration Utility to Evaluate the Double Integral ∫12∫0xexydydx\int _ { 1 } ^ { 2 } \int _ { 0 } ^ { x } e ^ { x y } d y d x∫12​∫0x​exydydx

Use a Symbolic Integration Utility to Evaluate the Double Integral $\int _ { 1 } ^ { 2 } \int _ { 0 } ^ { x } e ^ { x y } d y d x$