Math 181 sample problems for Hour Exam Two
Evaluate the following integrals, write clearly, and show your steps and method.
1.
Z1
x2
−3dx, Z1
x2+ 3 dx Z1
x2+ 5x+ 4 dx
Z1
x2+ 4x+ 5 dx Zx
x2+ 5x+ 4 dx Zx
x2+ 4x+ 5 dx
Zxsin x dx dx Zln x dx Zxln x dx
Zx2e−xdx Zxe−x2
dx Z1
√1−x2dx
2. Use the trapezoid rule and the midpoint rule with one interval (n=1) to estimate
Z1
1 + x2dx
.
3. Evaluate the improper integrals:
(a) R∞
0(1 + x)3/2dx.
(b) R∞
0x2e−xdx.
4. Calculate the length of the curve y=x3/2from x= 0 to x= 5.
5. Calculate the area of the surface obtained by rotating the curve y=x3from x= 0 to
x= 4 about the x-axis.
6. A fish tank is filled to a height of 1 foot with water which weighs 62.5 pounds per
cubic foot. One side is a vertical rectangular sheet of glass with 2 square feet below
the water level. What is the force of the water on this side? (Set up and evaluate an
integral.)
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