MACHAKOS UNIVERSITY
University Examinations 2019/2020 Academic Year
SCHOOL OF PURE AND APPLIED SCIENCES
DEPARTMENT OF MATHEMATICS AND STATISTICS
………..YEAR …… SEMESTER SPECIAL /SUPPLEMENTARY EXAMINATION FOR
BACHELOR OF …………………………….
ECU 200: ENGINEERING MATHEMATICS V
DATE: TIME:
INSTRUCTIONS TO CANDIDATES
Attempt question one (compulsory) and any other two questions.
QUESTION ONE (30 MARKS)
a) Calculate the length of the equiangular spiral r = ae kθ from θ = 0 to θ = 2π (3 marks)
b) Calculate the surface area of a sphere obtained by rotating x 2 + y 2 = a 2 between
x = − a and x = a about the x − axis (4 marks)
c) Determine the equation of a curve passing through the point 3,2 whose gradient is
5 − + 1 at every point , (4 marks)
d) Determine the centroid of the region bounded by x = x 2 and y = x between
x = 0 and x = 1 (4 marks)
e) Determine
dx
i. x + 16
2
(5 marks)
e
4x
ii. cos 2 x cos 4 x dx (5 marks)
3
(2 x + 3) dx
7
iii. (5 marks)
0
Examination Irregularity is punishable by expulsion Page 1 of 2
University Examinations 2019/2020 Academic Year
SCHOOL OF PURE AND APPLIED SCIENCES
DEPARTMENT OF MATHEMATICS AND STATISTICS
………..YEAR …… SEMESTER SPECIAL /SUPPLEMENTARY EXAMINATION FOR
BACHELOR OF …………………………….
ECU 200: ENGINEERING MATHEMATICS V
DATE: TIME:
INSTRUCTIONS TO CANDIDATES
Attempt question one (compulsory) and any other two questions.
QUESTION ONE (30 MARKS)
a) Calculate the length of the equiangular spiral r = ae kθ from θ = 0 to θ = 2π (3 marks)
b) Calculate the surface area of a sphere obtained by rotating x 2 + y 2 = a 2 between
x = − a and x = a about the x − axis (4 marks)
c) Determine the equation of a curve passing through the point 3,2 whose gradient is
5 − + 1 at every point , (4 marks)
d) Determine the centroid of the region bounded by x = x 2 and y = x between
x = 0 and x = 1 (4 marks)
e) Determine
dx
i. x + 16
2
(5 marks)
e
4x
ii. cos 2 x cos 4 x dx (5 marks)
3
(2 x + 3) dx
7
iii. (5 marks)
0
Examination Irregularity is punishable by expulsion Page 1 of 2
