calclus quiz, show all work

MAC 2312 Calculus 2

Quiz 1

Welcome to your first Quiz! For all questions, please show your work. This allows me to provide

helpful feedback and appropriately assign partial credit. Correct answers without supporting work

will not receive credit.

1) Find the exact area bounded by 𝑥 = −𝑦2 + 9 and 𝑥 = 1

2 𝑦2 − 6𝑦 − 9. Do not give a decimal

answer.

2) Find the exact area of the region bounded by 𝑦 = 𝑥2 and 𝑦 = √𝑥 for 0 ≤ 𝑥 ≤ 4. Do not give a

decimal answer.

3) For the following problems, SET UP- BUT DO NOT INTEGRATE the Integral representing the

volume generated by rotating the region bounded by the given curves between 𝑥 = −1 and

𝑥 = 1 about the indicated axis USING THE DISC/WASHER METHOD

The functions are: 𝑦 = √𝑥2 3

and 𝑦 = 1

x axis ______________________________________________________

y = -1 ______________________________________________________

y = 1 ______________________________________________________

4) For the following problems, SET UP- BUT DO NOT INTEGRATE the Integral representing the

volume generated by rotating the region bounded by the given curves about the indicated

axis USING THE SHELL METHOD

𝑦 = 𝑥2, 𝑦 = 2 − 𝑥2, and 𝑥 ≥ 0

y axis ______________________________________________________

x = -2 ______________________________________________________

x = 1 ______________________________________________________

5) Find the volume of the solid obtained by rotating the region bounded by 𝑦 = −𝑥2 + 6𝑥 − 8

and 𝑦 = 0 about the y-axis.

6) Find the volume of the solid obtained by rotating the region bounded by 𝑦 = −𝑥2 + 6𝑥 − 8

and 𝑦 = 0 about the x-axis.

7) Find the volume of the solid obtained by rotating the region bounded by 𝑥 = (𝑦 − 3)2 and

𝑥 = 4 about 𝑦 = 1.