haw a iyada aha sidaa ayaanu kau dirney

1. TIMO’ADE UNIVERSITY COLLEGE CALCULUS II MID-EXAM (20 MARKS)
1
Name; ------------------------------------------------ class; -----------------
Section one: Multiple choice questions
Circle the correct answer, each question carries 2 marks (Total of 10 marks).
1) Which of the following is equivalent to ∫
1
𝑢
𝑑𝑢 ?
A)
1
𝑢
+ 𝑐
B) ln|𝑢| + 𝑐
C) 0
D)
1
𝑢2
+ 𝑐
2) Evaluate ∫ (
3
1
3𝑥2
− 4𝑥 + 3)𝑑𝑥
A) 18
B) 20
C) 16
D) 54
3) What is the exact value of ∫ 𝑥 𝑒𝑥
𝑑𝑥 ?
A) 𝑥𝑒𝑥
+ 𝑒𝑥
+ 𝑐
B) 𝑥𝑒𝑥
− 𝑒𝑥
+ 𝑐
C) 𝑒𝑥
+ 𝑥𝑒𝑥
+ 𝑐
D) 𝑒𝑥
− 𝑥𝑒𝑥
+ 𝑐
4) Any rational function of x where 𝑓(𝑥) =
𝑝(𝑥)
𝑄(𝑥)
where both p(x) and Q(x) are
polynomials and the degree of p(x) is smaller than the degree of Q(x), could be
expressed as a sum of relatively simpler rational functions is called …………….
A) Substitution
B) Partial fractions
C) Trigonometric substitutions
D) By parts

2. TIMO’ADE UNIVERSITY COLLEGE CALCULUS II MID-EXAM (20 MARKS)
2
5) Integrating the expression ∫ 6𝑒2𝑥
𝑑𝑥 is the same as:
A) 12𝑒𝑥
+ 𝑐
B) 6𝑒2𝑥
+ 𝑐
C) 3𝑒2𝑥
+ 𝑐
D) 3𝑒𝑥
+ 𝑐
Section Two:Structured Questions (10 marks)
Answer only 2 questions for the following questions, show your answers clearly in the
space provided.
1. Integrate each of the following
a) ∫ 10𝑥(𝑥2
+ 3)4
𝑑𝑥 (2 marks)
b) ∫ 2𝑥𝑒𝑥2
𝑑𝑥 (3 marks)

3. TIMO’ADE UNIVERSITY COLLEGE CALCULUS II MID-EXAM (20 MARKS)
3
2. Evaluate
a) ∫
6
(𝑥+3)(𝑥+1)
𝑑𝑥 (3 marks)
b) ∫
2𝑥−1
𝑥2−𝑥−6
𝑑𝑥 (2 marks)
3. Find the integrals of the following
a) ∫ 2𝑥𝑒𝑥
𝑑𝑥 (3 marks)
b) ∫ 𝑥𝑠𝑖𝑛𝑥𝑑𝑥 (2 marks)

4. TIMO’ADE UNIVERSITY COLLEGE CALCULUS II MID-EXAM (20 MARKS)
4
4. Evaluate the following integrals
a) ∫ 𝑐𝑜𝑠𝑥𝑠𝑖𝑛3
𝑥𝑑𝑥 (3 marks)
b) ∫𝑡𝑎𝑛𝑥𝑑𝑥 (2 marks)
End