MATH 152 Activity 8 (Section 9.3-9.4)
Directions: Put both your name and your partners name on the answersheet. Use scratch paper for work, meaning only
put the answers on the answer sheet. Turn in only ONE answer sheet per pair. Calculators are allowed and you may
use your notes and textbook. Failure to follow these instructions will result in a 1 point deduction. Neat handwriting is
expected.
1. Find the length of the curve y =
1 2 1
x − ln x from x = 1 to x = 4.
4
2
√
3
2. Find the length of the curve y = 8 x2 from x = 0 to x = 1. Hint: Consider integrating with respect to y.
3. Find the length of the curve parametrized by x = t2 , y = 4t3 from t = −1 to t = 1.
4. Find the surface area obtained by rotating the curve y = 2x3 , 0 ≤ x ≤ 2 about the x axis.
5. Find the surface area obtained by rotating the curve y =
√
3
x, 1 ≤ y ≤ 2 about the y axis.
6. Find the surface area obtained by rotating the curve x = cos(2t), y = sin(2t), 0 ≤ t ≤
1
π
about the x axis.
4