I just took my Calculus II final and I have a question about this

[flyingpig]

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]

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.

 

[flyingpig]

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

 

[Mark44]

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

 

[flyingpig]

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?

 

[Leptos]

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 e^x2 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.