CALCULUS III
FINAL EXAM
Sample 2
Student Name: ___________________________________________
Student ID Number: ______________________________________
Course Title: Calculus III
Duration of Exam: 2 Hours
Number of Exam Pages: 7 pages (including this cover sheet)
Exam Type: Closed book
Total Mark: /30
Good luck 1|Page
,Exercise 1 (5 marks)
Using double integral in polar coordinates, set up the limits of integration to find the area
of the shaded region. (Do not evaluate.)
Good luck 2|Page
, Exercice 2 (5 marks)
1 1
Let 𝐼 = ∫0 ∫√𝑦 sin(𝑥 3 )𝑑𝑥𝑑𝑦.
1) Sketch the region of integration in xy-plane.
2) Reverse the order of integration.
3) Evaluate 𝐼.
Good luck 3|Page
FINAL EXAM
Sample 2
Student Name: ___________________________________________
Student ID Number: ______________________________________
Course Title: Calculus III
Duration of Exam: 2 Hours
Number of Exam Pages: 7 pages (including this cover sheet)
Exam Type: Closed book
Total Mark: /30
Good luck 1|Page
,Exercise 1 (5 marks)
Using double integral in polar coordinates, set up the limits of integration to find the area
of the shaded region. (Do not evaluate.)
Good luck 2|Page
, Exercice 2 (5 marks)
1 1
Let 𝐼 = ∫0 ∫√𝑦 sin(𝑥 3 )𝑑𝑥𝑑𝑦.
1) Sketch the region of integration in xy-plane.
2) Reverse the order of integration.
3) Evaluate 𝐼.
Good luck 3|Page
