Calc II Final Review

Page 1

Topics to Know for Calc. II Final

Integrals:

Two types: Definite and Indefinite

1. Definite: ∫ f(x) dx (b on top and a on the bottom)

Area below f(x) over the integral [a, b]. Answer is a definite number.

2. Indefinite: ∫ f(x) dx

Find the antiderivative of f. Answer is a function + C.

Page 2

Things to Put on Calc II Final Cheat Sheet

ln (1) = 0

1/(cos^2 θ) = sec^2 θ

list of derivatives/integrals from the 8/25 lecture

To find displacement: take the integral of the velocity function and solve it using the upper and lower bounds (bounds may be given as t=4 and t=1; from 1 to 4 seconds; or 0 < t <4 (I just used 1 and 4 as an example). Answer can be negative

To find distance: take the integral of the absolute value of the velocity function and solve using the bounds. To take the absolute value, graph the function nd shade the area above and below the line within the bounds. Anything below the z-axis is negative and anything above is positive. Take the integral as normal, with respect to the positive and negative aspects. Distance will ALWAYS be a positive number

When going from a rate to a single unit (like going from liters per minute to liters), take the integral of the rate function

p(x) = m'(x) (Linear density is equal to the integral of the change in mass (Mf-Mi)) (Mf is the upper bound and Mi is the lower)

When finding area between two curves that are sideways, take the integral of the rightmost - the leftmost