## Related questions with answers

Question

In the following exercise, use a graphing utility to approximate the iterated integral.

$\int_0^{\pi / 4} \int_0^4 5 r e^{\sqrt{r \theta}} d r d \theta$

Solutions

VerifiedSolution A

Solution B

Answered 10 months ago

Step 1

1 of 3$I=\int_0^{\pi/4}\int_0^45re^{\sqrt{r\theta}}\>drd\theta$ $\\ \\$$=$\dfrac{40(-6+\pi+2e^{\sqrt{\pi}}(3-3\sqrt{\pi}+\pi))}{\pi}$ \approx 87.131$

Answered 10 months ago

Step 1

1 of 7We will evaluate the iterated integral
using a computer algebra system (*Mathematica*).

In general, the code for evaluating a double integral

$\int_a^b \int_{g_1(x)}^{g_2(x)}f(x,y)\,dy\,dx$

is as follows:

```
NIntegrate[f(x,y), {x, a, b}, {y, g1(x), g2(x)}]
```

In other words, when we write the function $f$, we first write the limits of the external integral and by which variable the external integral is integrated. Then we write the limits for the internal integral.

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