Calculus homework help

MAC 2311 Review for Unit # 5 Test
Name___________________________________
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Find the area enclosed by the given curves. 1) y = 2x – x2, y = 2x – 4 1)
2) y = 1 2
x2, y = -x2 + 6 2)
Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis.
3) y = x, y = 0, x = 1, x = 5 3)
4) y = 2x + 3 , y = 0, x = 0, x = 1 4)
5) y = – 6x + 12, y = 6x, x = 0 5)
6) y = x2 + 2, y = 4x + 2 6)
Find the volume of the solid generated by revolving the region about the y-axis.
7) The region enclosed by x = 4 y , x = 0, y = 1, y = 6 7)
Use the shell method to find the volume of the solid generated by revolving the shaded region about the indicated axis.
8) About the y-axis
x = 3
x1 2 3 4 5 6
y 6
5
4
3
2
1
x1 2 3 4 5 6
y 6
5
4
3
2
1
y = 3x
8)
Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines about the y-axis.
9) y = x2, y = 5 + 4x, for x ≥ 0 9)
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Find the volume of the solid generated by revolving the region about the given axis. Use the shell or washer method. 10) The region bounded by x = 5 y, x = – 5y, and y = 1 about the line y = 1 10)
11) The region in the first quadrant bounded by x = 6y – y2 and the y-axis about the x-axis 11)
Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves about the given lines.
12) y = 4x, y = 0, x = 2; revolve about the x-axis 12)
Find the average value of the function over the given interval. 13) f(x) = 2x + 6 on [-3, 3] 13)
BONUS QUESTION COVERING 6.5 WORK – PLEASE LOOK OVER THIS SECTION
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Answer Key Testname: MAC 2311 UNIT # 5 TEST
1) 32 3
2) 16
3) 1243 π
4) 4π 5) 72π
6) 8965 π
7) 403 π
8) 108 5 π
9) 875 6 π
10) 133 π
11) 216π
12) 128 3 π
13) 6
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