# MATH 152 Activity 5 (6.4-8.2) ```MATH 152 Activity 5 (6.4-8.2)
Directions: Put your group name, section number and members present on one answer sheet. Use
scratch paper for work, meaning only put the answers on the answer sheet. Turn in only ONE answer
sheet per group. No calculators allowed, however you may use your notes and textbook. Failure to
follow these instructions will result in a 1 point deduction. Neat handwriting is expected.
1.
Write (but do NOT compute) an integral to find the area enclosed by y = 1 − x2
and y = x2 + x.
.
2.
Given f (x) = 3x2 −2x, find all values c ∈ [−1, 1] such that f (c) = favg , the average
value of f on this interval.
.
3.
ˆ
sin2 x cos2 x dx.
Calculate
.
4.
ˆ
2
x ln x dx.
Compute
1
.
5.
A 15-Newton weight is suspended vertically at the end of a 30 m long rope. The
rope weighs 6 Newtons. How much work (in N-m) is required to pull the weight
to the top?
.
6.
Given function f and g with 0 ≤ g(x) ≤ f (x) on the interval 0 ≤ x ≤ 2, write an
integral to compute the volume of the solid formed by rotating the region bounded
by y = f (x), y = g(x), x = 0, and x = 2 about the line y = −1.
.
7.
ˆ
Calculate
2
.