Cracking The Ap Calculus ab Exam 2018

As you can see, these integrals are pretty straightforward. The key is to use u-substitution to transform
nasty-looking integrals into simple ones.

There’s another type of exponential function whose integral you’ll have to find occasionally.

∫a

u   du

As you should recall from your rules of logarithms and exponents, the term au can be written as e u ln a.

Because ln a is a constant, we can transform into ∫au du into ∫e ulna du. If you integrate this, you’ll get

Now substituting back au for e u ln a,

∫a

u   du  =   au  +   C

Example 17: Find ∫ 5 x dx.

Follow the rule we just derived.

∫^5

x dx    =       5 x +   C

Because these integrals don’t show up too often on the AP Exam, this is the last you’ll see of them in this
book. You should, however, be able to integrate them using the rule, or by converting them into a form of

∫e

u   du.

Try these on your own. Do each problem with the answers covered, and then check your answer.

PROBLEM 4. Evaluate

Answer: Move the constant term outside of the integral, like this.