Integrals

Topics in this chapter

• Standard Indefinite Integrals
• Trigonometric Integral Techniques
• Substitution and Integration by Parts
• Partial Fractions and Rationalisation
• Definite Integrals and Properties
• Fundamental Theorem of Calculus
• Areas Between Curves

Cheat sheet

Practice questions

1. Question 1Q-3692FB

   Evaluate ∫ x/(x² + 1) dx.

   1. A.ln(x² + 1) + C
   2. B.(1/2)ln(x² + 1) + C
   3. C.1/(x² + 1) + C
   4. D.tan⁻¹x + C
   See the answer and solution
2. Question 2Q-314E31

   The value of ∫₀¹ (3x² + 2x + 1) dx is:

   1. A.2
   2. B.5/2
   3. C.3
   4. D.7/2
   See the answer and solution
3. Question 3Q-44BCC1

   Evaluate ∫₀¹ x ln(1 + x²) dx.

   1. A.ln 2 − 1/2
   2. B.ln 2 + 1/2
   3. C.1/2 − ln 2
   4. D.ln 2
   See the answer and solution
4. Question 4Q-48214D

   Find ∫ x²/(x² + 1) dx.

   See the answer and solution
5. Question 5Q-DCDE10

   Evaluate ∫ sec²(3x) dx.

   1. A.tan(3x) + C
   2. B.(1/3)tan(3x) + C
   3. C.3tan(3x) + C
   4. D.sec(3x) + C
   See the answer and solution