calculus II

Midterm 01

Course Code: 021 Course Name: Calculus II

Student Name:

Total Score:

Obtained Score:

Date: July 8, 2020

Solve each question below by showing all the necessary steps. (20%)

Note:

1. All students need to download this midterm, then after solving

on it you need to scan it and make a pdf file then upload into

the online system.

2. Uploading Pictures or anything else with mobile phone is not

acceptable at all.

3. Deadline for submission of the (Midterm 01) is July 13, 2020

till 19:00 late submission will not be entertained.

4. Solve each question below by showing all the necessary steps.

5. If still you have any problem you can ask me via e-mail.

Solve the entire questions:

Question 01:

Find the area of the surface obtained by rotating the curve about

the y-axis:

10 ,2 2

 yyyx

Question 02:

Use cylindrical shells to find the volume of the solid obtained by

rotating about the y-axis the region bounded by y = 4 - x2 and

between y = x, and x = 0.

Question 03:

Find the length of the arc of the semi cubical parabola y2 = x3

between the points (1, 1) and (4, 8).

Question 04:

Find the area of the surface obtained by rotating the curve about

the x-axis:

80 ,44 2

 xxy

Question 05:

Integrate by parts:

Question 06:

Integrate by trigonometric integral formulas.

2 2 sin ( ) cos ( )d  

Question 07:

Integrate by using trigonometric substitution.

i.

ii.

iii.

2 2

dx

x x 

Question 08:

Integrate by using Partial Fraction.