Section 7.3 Tables of Integrals
1.
a. Use Integration by Parts to find the anti-derivative of
x 6 ln x dx
y x 6 ln x
1 7
1 7
x ln x
x C
7
49
b. Look at the #13 in the table in Integrals. What is the
Section 8.1 Areas and Volumes
1. Write a Riemann sum and then a definite integral representing the area of the region, using the
strip shown. Evaluate the integral exactly.
3y 4 y2
1
dy
4
4
4
1
4
1 3
Project for 7.5 and 7.6
Approximating Definite Integrals and Approximation Errors
Left rule, Right rule, Midpoint rule, Trapezoid rule, and Simpsons rule
You encountered ways to approximate the value
Section 7.7 & 7.8 Improper Integrals
1. Calculate the integral, if it converges.
1
1
2
x 1
1
dx lim
b
x 1
b 1
2. For what values of
1
2
p
1
x2 1
dx
b
dx lim arctan x |1 lim arctan b arctan1
b
b