1 2 Construction Engineering
Resume:
EMT ***: Calculus with Analysis
Instructions
1. Students are to provide detailed solution to the following questions according to the groupings. [4 Marks]
2. Students are to type the solutions using MS WORD and its associated mathematics tools. [10 Marks]
3. Using font size of 12 and double spacing. [2 Marks] 4. Save the document as the group name. E.g. GROUP 1, GROUP 2, etc. [2 Marks] 5. Submit the soft copy through ********@*****.*** straight from the computer on or before 22
nd
July, 2025, by 3:00 pm. NB: PDF will NOT be accepted. [2 Marks] GROUP 1
Evaluate the following integrals
1. 3(2 + 4)5
2. 2 3 + 1
3.
(1 − 6 )4
4. cos3 sin
5.
sec2(
1
)
2
6.
2 − 2 − 1
( − 1)2( 2 + 1)
7. Find the Eigen-values and its corresponding eigenvectors for the matrix = 2 0 0
0 3 4
0 4 9
.
GROUP 2
Evaluate the following integrals
1. sin 2
2. 2( 3 + 5)9
3. (3 − 2)20
4. (3 + 2)2.4
5. + 1 2 + 2
6.
+ 4
2 − 2 + 5
7. Find the Eigen-values and its corresponding eigenvectors for the matrix = 1 1 −2
−1 2 1
0 1 −1
.
Page 2 of 8
GROUP 3
Evaluate the following integrals
1.
( 2 + 1)2
2.
5 − 3
3. sin
4.
2 + 1
5.
+ 2
3 + 3
6.
3 2 + + 4
4 + 3 2 + 2
7. Find the Eigen-values and its corresponding eigenvectors for the matrix = 1 2 2
0 2 1
−1 2 2
.
GROUP 4
Evaluate the following integrals
1.
4 2 − 7 − 12
+ 2)( − 3)
2
1
2.
2 + 2 − 1
3 −
3.
1
( + 5)2( − 1)
4.
2 − 5 + 16
(2 + 1)( − 2)2
5.
3 + 4
2 + 4
6.
2( − 1)2
GROUP 5
Evaluate the following integrals
1. (1 + tan )5 sec2
2. 1 +
3. cos sin
4.
22
3 1 + 3
5.
tan−1
1 + 2
6.
1
3 − 1
7. Find the Eigen-values and its corresponding eigenvectors for the matrix = 1 2 3
0 2 3
0 0 3
.
Page 3 of 8
GROUP 6
Evaluate the following integrals
1. tan sec2
2.
sin
3.
cos
sin2
4.
+ 1
5. cot csc2
6. Solve the system of equation using cramer’s rule; 3 + 4 − 3 = −2
−2 + 3 − = −1
2 + − 2 = 6
GROUP 7
Evaluate the following integrals
1.
cos
л
2
2.
sin 2
1 + cos2
3.
sin
1 + cos2
4. sec2
4
л
0
5. csc л cot л
1
2
1
5
6. Solve the system of equation using cramer’s rule;
−3 + + = −4
− + 2 − 2 = 1
2 − − = −1
Page 4 of 8
GROUP 8
Evaluate the following integrals
1. tan3
л
6
−
л
6
2. 2
1
0
3.
1
2
2
1
4.
2 sin
1 + 6
л
2
−
л
2
5.
3 (1 + 2 )2
13
0
6. cos sin(sin )
л
2
0
7. Solve the system of equations using cramer’s rule; 2 − 5 + 3 = 8
3 − + 4 = 7
+ 3 + 2 = −3
GROUP 9
Evaluate the following integrals
1. 2 + 2 ( > 0)
1
0
2. 2 − 2
0
3. − 1
2
1
4.
1 + 2
4
0
5.
6. Find the eigenvalues and its corresponding eigenvectors for the matrix = 2 −3 0
2 −5 0
0 0 3
.
Page 5 of 8
GROUP 10
Evaluate the following integrals
1.
+ 1
+
1
0
2. sin
2л
−
2
0
3.
sin−1
1 − 2
1
2
0
4. 2
5. cos
7. Solve the system of equation using cramer’s rule; 2 1 − 2 + 3 = 5
1 + 2 + 3 = 9
4 1 + 2 − 3 = 7
GROUP 11
Evaluate the following integrals
1. cos5
2.
2
3. 2sinл
4. 2 + 1
5.
6. Solve the system of equation using matrix invertible approach; 2 1 − 2 + 3 = 5
1 + 2 + 3 = 9
4 1 + 2 − 3 = 7
Page 6 of 8
GROUP 12
Evaluate the following integrals
1. sin 2
2. 2cos
3. sin−1
4. arctan4
5. sec2 2
6. 2
7. Solve the system of equations using matrix invertible approach; 2 − 5 + 3 = 8
3 − + 4 = 7
+ 3 + 2 = −3
GROUP 13
Evaluate the following integrals
1. 20 sin 3
2. sin 3
л
0
3. cosh
1
0
4.
2
2
1
5. 5
6. Solve the system of equation using matrix invertible approach;
−3 + + = −4
− + 2 − 2 = 1
2 − − = −1
Page 7 of 8
GROUP 14
Evaluate the following integrals
1. sinh
2. cos2
3. 2 + 1
1
0
4.
9
4
5. 3 cos
л
0
6. Solve the system of equation using matrix invertible approach; 3 + 4 − 3 = −2
−2 + 3 − = −1
2 + − 2 = 6
GROUP 15
Use integral by parts to prove the reduction formula. 1. −1 2. = − 1
3. tan =
tan −1
− 1
− tan −2 ( 1)
4. sec =
tan sec −2
− 1
+
− 2
− 1
sec −2 ( 1)
5. Solve the system of equation by matrix inversion; 2 1 + 2 + 2 3 = 0
2 1 − 2 + 3 = 10
1 + 3 2 − 3 = 5
Page 8 of 8
GROUP 16
Evaluate the following integrals
1. sec 2 tan 2
2. 2
3.
+
( 0)
4.
cos
5. sin 1 +
3
2
6. cos sin6
7.
2 − 4 − 13
1
0
8. Find the Eigen-values and its corresponding eigenvectors for the matrix = 1 4 2 3
.
GROUP 17
Evaluate the following integrals
1.
5 2 + 3 − 2
3 − 2 2
2.
2 − + 6
3 − 3
3.
10
( − 1)( 2 − 9)
4.
2 + + 1
( 2 − 1)2
5.
3 + 2 + 2 + 1
( 2 − 1)( 2 + 2)
GROUP 18
Evaluate the following integrals
1.
1
2 − 1
3
2
2.
− 1
2 + 3 + 2
1
0
3.
2 −
4.
1
5.
3 − 2 2 − 4
3 − 2 2
4
3
6.
3 − 4 − 10
2 − − 6
1
0
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