Differentiation and Integration

As I tell my calculus students, differentiation is a science. There are rules to follow, but if you follow them carefully, you can compute the derivative of anything. This leads to one of my favorite classroom activities. However, integration is as much art as science; for example, see my series on different techniques for computing

\displaystyle \int_0^{2\pi} \frac{dx}{\cos^2 x + 2 a \sin x \cos x + (a^2 + b^2) \sin^2 x}

The contrast between differentiation and integration was more vividly illustrated in a recent xkcd webcomic:

Source: https://xkcd.com/2117/

Leave a comment

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.

%d bloggers like this: