Math 172
Practice Final D
• The final exam is scheduled for 10-11:50 on Friday in ROBH 101.
• Make sure you have done and reviewed all of the Chapter 11 homework.
• Make sure you have done and reviewed all 20 of the review integrals posted on the course webpage.
• I will be in the MLC 4-6 Tuesday and 3-6 Thursday.
• I will be in the office Tuesday 2-4, Thursday 2-3, and other times by appointment, just send me
an email and we can work something out.
• I am holding review sessions 6 - 7:50 Tuesday, ROBH 101 and 4-5:50 Wednesday, JOHN 339.
1. Integrate.
Z
(x + 1) ln x
(a)
dx [HINT:split into two parts]
x2
Z √
4 − x2
dx
(b)
x
2. Express 1 + cos t, cos3 t in the form y = f (x).
Z
sin3 θ cos θ dθ
Z
5x + 7
dx
(x + 1)(x + 2)
(c)
(d)
3. Consider the curve (e−t cos t, e−t sin t)
(a) Find the length of the path over 0 ≤ t ≤ 1
(b) Find the speed of a particle traveling along the curve at t = 0.
dy
(c) Find the direction, dx
, of a particle traveling along the curve at t = 0.
4. Convert to an equation in rectangular coordinates. r =
2
3 sin θ+4 cos θ
5. Find the length of the polar curve r = eθ for 0 ≤ θ ≤ 2π.
6. Find the area inside both r = sin θ and r = cos θ. See the figure.
0
0.5
1