MACHAKOS UNIVERSITY
University Examinations 2020/2021 Academic Year
SCHOOL OF PURE AND APPLIED SCIENCES
DEPARTMENT OF MATHEMATICS AND STATISTICS
SECOND YEAR SPECIAL /SUPPLEMENTARY EXAMINATION FOR
BACHELOR OF SCIENCE (ELECTRICAL AND ELECTRONICS ENGINEERING)
BACHELOR OF SCIENCE IN (MECHANICAL ENGINEERING)
BACHELOR OF SCIENCE IN (CIVIL ENGINEERING)
ECU 200: ENGINEERING MATHEMATICS V
DATE: 22/3/2021 TIME: 8.30-10.30 AM
INSTRUCTIONS TO CANDIDATES
Attempt Question ONE and any other TWO questions.
QUESTION ONE (30 MARKS)
a) State the fundamental theorem of Integral Calculus. (1 mark)
b) Find the following integrals:
3x + 1
i. ( x − 1)( x 2
+ 1)
dx (4 marks)
π
6 x sin( x
2
ii. ) dx (4 marks)
0
sin
4
iii. t cos tdt (3 marks)
c) Find the number c that satisfies the mean value theorem of integral calculus for the function
1
y= over the interval [0 , 1]. (3 marks)
2x + 1
x
2
d) Determine the double integral ydydx . (2 marks)
e) Given Ae x + Be − x = 4 cosh x − 5sinh x . Determine the values of A and B. (3 marks)
Examination Irregularity is punishable by expulsion Page 1 of 3
University Examinations 2020/2021 Academic Year
SCHOOL OF PURE AND APPLIED SCIENCES
DEPARTMENT OF MATHEMATICS AND STATISTICS
SECOND YEAR SPECIAL /SUPPLEMENTARY EXAMINATION FOR
BACHELOR OF SCIENCE (ELECTRICAL AND ELECTRONICS ENGINEERING)
BACHELOR OF SCIENCE IN (MECHANICAL ENGINEERING)
BACHELOR OF SCIENCE IN (CIVIL ENGINEERING)
ECU 200: ENGINEERING MATHEMATICS V
DATE: 22/3/2021 TIME: 8.30-10.30 AM
INSTRUCTIONS TO CANDIDATES
Attempt Question ONE and any other TWO questions.
QUESTION ONE (30 MARKS)
a) State the fundamental theorem of Integral Calculus. (1 mark)
b) Find the following integrals:
3x + 1
i. ( x − 1)( x 2
+ 1)
dx (4 marks)
π
6 x sin( x
2
ii. ) dx (4 marks)
0
sin
4
iii. t cos tdt (3 marks)
c) Find the number c that satisfies the mean value theorem of integral calculus for the function
1
y= over the interval [0 , 1]. (3 marks)
2x + 1
x
2
d) Determine the double integral ydydx . (2 marks)
e) Given Ae x + Be − x = 4 cosh x − 5sinh x . Determine the values of A and B. (3 marks)
Examination Irregularity is punishable by expulsion Page 1 of 3
