MA113_2010SPRING_EXAM1__[0] - MA113(Calculus II Midterm...

MA113 (Calculus II) - Midterm Examination # 1
March 2, 2010
4:05pm-5:55pm
Write your name on your exam sheet AND booklet(s), and please show all work. The
exam is out of 100 points.
1. [30 pts.] Set up, but do not solve integrals that calculate the desired quantity (you
don’t need to start from first principles and do rigorous derivations (i.e., Riemann
sums, etc.), but pictures and word explanations may be helpful in determining partial
credit, and should definitely accompany your solutions).
(a) [3 pts.] the arclength of the curve r =
1
θ 2
for θ ≥ π/ 2
(b) [4 pts.] the volume of the solid obtained by revolving the portion of the graph
of y = x
4
+ x + 1 above - 1 ≤ x ≤ 1 about the line x = - 1
(c) [4 pts.] the volume of the solid obtained by revolving the portion of the graph
of x =
1
√
y
above 2 ≤ x ≤ 3 about the x -axis
(d) [4 pts.] the area of the intersection between the region bounded by r = 2 cos 3 θ
and the region bounded by r = 1
(e) [5 pts.] the coordinates of the centroid of the triangle with vertices ( - 2 , 0),
(1 , 3), and (1 , 4)
(f) [5 pts.] the surface area swept out when the upper half (