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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