MATH 1372, SECTION 33, FINAL REVIEW 1. Convert the following integral to an integral with variable using the substitution 3x = 4 tan .
4 3/3
4/3
x dx 16 + 9x2
2. Find the following antiderivative showing all steps: x dx 24 x
3. If the following integral
6541 First Moments
1. The region bounded by the curve y = 5a: £132 and the 3: axis is covered
by a lamina of constant density p. Find Mac, the rst moment of this lamina
about the ac axis. Find My, the rst moment of this lamina about the y
axis. Find the
6531 Arc Length
1. Find the arc length of the curve whose equation is y = (1/8):I:2 lnzr
from the point (1, 1 / 8) to the point (4, 2 1n 4).
2.
1+ <s>1= \+ tXt+§a = (2 + 3%)
4- 2 H-
x .L -23.
SI + xydx .- .8 +94%
:gog-FJIALIL
I
2. Find the arc