AP Calculus AB 1 Multiple Choice 7

These videos are the worked out solutions to an entire practice AP test


The videos are recorded so that you can pause the video and solve the problem before watching the solution or you can download the entire test, above, and only watch the videos you need to watch.

I hope this helps more people get some 5s.

[djdmath]

and we can see that the \frac{1}{\sqrt{x}} will cancel out, with a 2 coming out of the integral.

My best recommendation for getting better at this is to just practice practice practice. Eventually, it will become second nature to determine what we should choose as u. In addition, you will get faster at determining when u-substitution won't work (meaning that you should try integration by parts, partial fractions, or some other integration method).

[djdmath]

That really is the difficult part of u-substitution.

I often tell my students to look at the inner-most function and see if its derivative is multiplied to the rest of the integrand. In this case, we can see that in \frac{1}{\sqrt{x}e^{\sqrt{x}}, the inner most function is the \sqrt{x} as the exponent of e. It just so happens that the derivative of \sqrt{x}, \frac{1}{2\sqrt{x}} almost shows up multiplied to the rest of the integrand. Because of this, we can substitute to get e^u