Section 7.3 Tables of Integrals
1.
a. Use Integration by Parts to find the antiderivative 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 value of
n
for part (a)?
n6
c. Explain how the formula
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 2
y 3
3 y 4 y dy y 4 y
4 2
3
1
4
2
4

1
125
5.2083
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 of a definite integral in Calculus I,
looking at a Riem
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
2 4 4
does the intergral below converge or diverge? Wh