 |
CLS601S - CALCULUS 2 - 2ND OPP - JULY 2023 |
|
|
1 Page 1 |
▲back to top |
(
nAmlBIA unlVERSITY
OF SCIEnCE Ano TECHnOLOGY
FACULTYOF HEALTH,NATURALRESOURCESAND APPLIEDSCIENCES
SCHOOLOF NATURALAND APPLIEDSCIENCES
DEPARTMENT OF MATHEMATICS, STATISTICS AND ACTUARIAL SCIENCE
QUALIFICATION: Bachelor of science in Applied Mathematics and Statistics
QUALIFICATION CODE: 07BSAM
COURSE CODE: CLS6015
LEVEL: 6
COURSE NAME: CALCULUS2
SESSION: JULY2023
DURATION: 180 MINUTES
PAPER:THEORY
MARKS: 100
SUPPLEMENTARY/SECOND OPPORTUNITYQUESTION PAPER
EXAMINERS
MR BENSON OBABUEKI
DR SERGE NEOSSI-NGUETCHUE
MODERATOR:
DR DAVID IIYAMBO
INSTRUCTIONS
1. Answer ALL questions in the booklet provided.
2. Show clearly all the steps used in the calculations.
3. All written work must be done in blue or black ink and sketches must
be done in pencil.
PERMISSIBLEMATERIALS
1. Non-programmable calculator without a cover.
THIS QUESTION PAPER CONSISTS OF 2 PAGES (excluding this front page)
|
|
2 Page 2 |
▲back to top |
(
Question 1 {29 marks)
Determine the following indefinite integrals using the indicated techniques:
1.1
(7)
1.2
f-4Xx3+--Xd3x
by partia. l fractio. ns.
(7)
1.3
f 2dx
? by trigonometric substitution.
4-144x-
(8)
f 1.4
sin3 a cos4 ada.
(7)
Question 2 {10 marks)
2.1 Determine the area enclosed by y = x2 -9 and y = 3x+ 9.
(5
2.2 Calculate the volume of the solid generated if y = cos 0 is rotated about the 0-axis
through a complete revolution, 0 0 -f.
(5)
Question 3 {14 marks)
fI
The definite integral ex2+3dx is to be estimated using the Trapezoidal Rule, correct to within an
0
error of 0.5.
3.1 Determine the number of subintervals needed.
(6)
3.2 Use n = 8 to estimate the given definite integral.
(8)
Question 4 {19 marks)
4.1 Determine the position of the centroid of the plane figure bounded by y = e2x, the x-
axis, the y-axis and the ordinate x = 2.
(9)
Page 1 of 2
|
|
3 Page 3 |
▲back to top |
4.2 Consider the parametric curve given by x = t 2 and y = 4t 2 -t 4 in the interval O t 2.
f1=2
4.2.1 Determine the area under the given curve using f(t)g'(t)dt.
(5)
t=O
fx=?
4.2.2 Determine the area under the given curve using ydx.
(5)
x=?
Question 5 (15 marks)
5.1
f xi
Using the infinite series approach, determine the indefinite integral !!__dx. (Hint
X
(7)
5.2 Determine the surface area of the solid generated by rotating the parametric curve
x = cos3 0, y = sin3 0 0 0 f about the -axis.
(8)
Question 6 (13 marks)
6.1 Convert y2+ (x -5)2 = 25 to polar coordinates.
(6)
6.2 Convert r = sin 20 to rectangular coordinates.
(7)
End of paper
Total marks: 100
Page 2 of 2