## Homework Statement

I spoke to a few people and pretty much everyone but me seem to know what is going on with a few questions. This question was one of the ones I stared blankly for a few minutes and then wrote down an answer

$$\int_{0}^{2} e^{x^2} d\theta$$

## The Attempt at a Solution

Look, it is with respect to theta, no x (not that you can even integrate it if it is x...)

I read some MVC on my own so I didn't have "too much" trouble with it, but I just wondered why it was put on a Calc II exam...

I asked the professor if it was a typo (twice) and he shooked his head saying "nope".

So solving you should get $$2e^{x^2}$$

Now my question is, (well I have more than one...)

1. Am I right?
2. If not, what single variable calculus techniques do you use to find the solution?

Mark44
Mentor

## Homework Statement

I spoke to a few people and pretty much everyone but me seem to know what is going on with a few questions. This question was one of the ones I stared blankly for a few minutes and then wrote down an answer

$$\int_{0}^{2} e^{x^2} d\theta$$

## The Attempt at a Solution

Look, it is with respect to theta, no x (not that you can even integrate it if it is x...)

I read some MVC on my own so I didn't have "too much" trouble with it, but I just wondered why it was put on a Calc II exam...

I asked the professor if it was a typo (twice) and he shooked his head saying "nope".

So solving you should get $$2e^{x^2}$$

Now my question is, (well I have more than one...)

1. Am I right?
2. If not, what single variable calculus techniques do you use to find the solution?

1. Yes.

Good, lol. Why the hell did my professor put up this kind of question on the exam anyways?

Mark44
Mentor
To see if you were paying attention to details such as the variable of integration, θ. Apparently you were paying attention.

Even if you weren't paying attention how could you integrate e^(x^2)? Also, how could a Cal II student know to treat e^(x^2) as a constant and not a variable?

Even if you weren't paying attention how could you integrate e^(x^2)? Also, how could a Cal II student know to treat e^(x^2) as a constant and not a variable?
Because it's a non-elementary integral and thus they should rub their eyes and take a second look at the question? It's well known result that ex2 and e-x2 cannot be evaluated analytically. This is a matter of paying attention to what you're doing rather than plugging and chugging(even if it's a cookbook course). We know that the dependent variable is whatever we're integrating with respect to, and everything else(not containing the dependent variable) can be held constant.