MACHAKOS UNIVERSITY
University Examinations for 2021/2022 Academic Year
SCHOOL OF PURE AND APPLIED SCIENCES
DEPARTMENT OF MATHEMATICS AND STATISTICS
SECOND YEAR FIRST SEMESTER EXAMINATION FOR
BACHELOR OF SCIENCE (ELECTRICAL AND ELECTRONIC ENGINEERING)
BACHELOR OF SCIENCE (MECHANICAL ENGINEERING)
BACHELOR OF SCIENCE (CIVIL ENGINEERING)
ECU 200: ENGINEERING MATHEMATICS V
DATE: 6/12/2021 TIME: 11:00 – 1:00 PM
INSTRUCTIONS: Attempt Question ONE and any other TWO questions.
QUESTION ONE (30 MARKS)
a) Differentiate between an Indefinite and a definite integral. (2 marks)
b) Determine the following integrals:
i. (2 marks)
2
x2
ii. 0 x 3 − 1 dx (4 marks)
dx
iii. x 2
+3
(4 marks)
c) Find the number c that satisfies the mean value theorem of integral calculus for the
1
function y = over the interval [0 , 1]. (3 marks)
2x + 1
x
2
d) Determine the double integral ydydx . (2 marks)
x 2 + 3x − 4
e) Determine lim 2 (2 marks)
x →1 x − 7 x + 6
Examination Irregularity is punishable by expulsion Page 1 of 3
University Examinations for 2021/2022 Academic Year
SCHOOL OF PURE AND APPLIED SCIENCES
DEPARTMENT OF MATHEMATICS AND STATISTICS
SECOND YEAR FIRST SEMESTER EXAMINATION FOR
BACHELOR OF SCIENCE (ELECTRICAL AND ELECTRONIC ENGINEERING)
BACHELOR OF SCIENCE (MECHANICAL ENGINEERING)
BACHELOR OF SCIENCE (CIVIL ENGINEERING)
ECU 200: ENGINEERING MATHEMATICS V
DATE: 6/12/2021 TIME: 11:00 – 1:00 PM
INSTRUCTIONS: Attempt Question ONE and any other TWO questions.
QUESTION ONE (30 MARKS)
a) Differentiate between an Indefinite and a definite integral. (2 marks)
b) Determine the following integrals:
i. (2 marks)
2
x2
ii. 0 x 3 − 1 dx (4 marks)
dx
iii. x 2
+3
(4 marks)
c) Find the number c that satisfies the mean value theorem of integral calculus for the
1
function y = over the interval [0 , 1]. (3 marks)
2x + 1
x
2
d) Determine the double integral ydydx . (2 marks)
x 2 + 3x − 4
e) Determine lim 2 (2 marks)
x →1 x − 7 x + 6
Examination Irregularity is punishable by expulsion Page 1 of 3
