Math 1210
Quiz 11
Due April 21st, 2014
This is a take-home quiz and it is due on Monday, April 21st. The value of
every question is indicated at the beginning of it. Please print this sheet and
write your answers in the space provided.
Name:
UID:
1. (20 points) For each of the following curves, write down the integral that would compute
its arc length.
(i) (5 points) y =
x4 +3
,
6x
x = 1,
(ii) (5 points) 30xy 3 − y 8 = 15,
(iii) (5 points) x = 3t2 + 2,
(iv) (5 points) y(x) =
x = 3.
y = 1,
y = 2t3 − 21 ,
Rx√
u3 − 1 du,
1
y = 3.
1 ≤ t ≤ 4.
1 ≤ x ≤ 2.
2. (10 points) Write down the integral that would compute the area of the surface generated
by revolving the following curves about the x-axis.
√
(i) (5 points) y = 25 − x2 , −2 ≤ x ≤ 3.
(ii) (5 points) x = r cos t,
y = r sin t,
0 ≤ t ≤ π (where r is any real number).
3. (5 points) Find the centroid of the region bounded by the curves
√
y = 3x − 4, y = 2 x, x = 1
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