Integral Calculus

Overview

Integral calculus finds antiderivatives and areas; definite integrals give accumulated quantities.

Key points

• ∫ xⁿ dx = xⁿ⁺¹/(n + 1) + C (n ≠ −1).
• ∫ (1/x) dx = ln |x| + C; ∫ eˣ dx = eˣ + C.
• ∫ sin x dx = −cos x + C; ∫ cos x dx = sin x + C.
• Integration by parts: ∫ u dv = uv − ∫ v du.
• A definite integral from a to b equals F(b) − F(a).
• Area under a curve is a definite integral (taking sign into account).

Practice MCQs

1. From the perspective of definition and scope, which one of the following statements about Integral Calculus is correct?

   1. Integral Calculus has no exceptions or limitations in exam analysis.
   2. Integral Calculus questions reward a formula-first approach and accurate algebraic manipulation.
   3. Do not apply a memorized Integral Calculus formula without checking its conditions.
   4. Integral Calculus is unrelated to institutions, processes or real-world applications.

   Read chapter notes · Similar questions

   Show answer

   Answer: (b) Integral Calculus questions reward a formula-first approach and accurate algebraic manipulation.. Integral Calculus questions reward a formula-first approach and accurate algebraic manipulation.

   Save for revision I got it right I got it wrong

2. Consider the following statements on Integral Calculus, focusing on definition and scope: 1. Integral Calculus questions reward a formula-first approach and accurate algebraic manipulation. 2. Check domains, signs and units before finalizing the option. Which of the statements given above is/are correct?

   1. 1 only
   2. 2 only
   3. Both 1 and 2
   4. Neither 1 nor 2

   Read chapter notes · Similar questions

   Show answer

   Answer: (c) Both 1 and 2. Both statements are correct.

   Save for revision I got it right I got it wrong

More topics in this chapter

• Vector Algebra
• Elementary Statistics
• Elementary Probability