| Calculus II Test #1 |
A/ Evaluate the following integrals
( solutions )
| 1) |
2) |
3) |
| 4) |
5) |
6) |
(24)
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B/ Draw a diagram for and solve each of the following
1) Find the area of the region bounded by y = x 2 and y = 2 – x 2.
2) Find the area of the region bounded by the graphs of x = 2y , y = 2x – 6, and y = 0.
3) Find the area of the region bounded by x = y 2 – 1 and x = y + 1.
(12)
C/ Draw a diagram for questions 1 and 2 and solve
1) Use Disk Method to evaluate the volume of the solid obtained by
revolving the region bounded by y = x 2 and y = x 3 , about:
| a) the x-axis | b) the y-axis |
(7)
2) Use Shell Method to find the volume of the solid obtained by
revolving the region between x = y 2 , x = 3 , and y = 0 about the y-axis.
(3)
3) Find z if z satisfies the hypothesis of the Mean Value Theorem
for Definite Integrals if f (x) = 3x 2 – 4x + 1 with a = 1 and b = 4.
(4)
TOTAL = 50
( Calculus II MathRoom Index )
