Table of contents

0. Functions7h 52m
1. Limits and Continuity2h 2m
2. Intro to Derivatives1h 33m
3. Techniques of Differentiation3h 18m
4. Applications of Derivatives2h 38m
5. Graphical Applications of Derivatives6h 2m
6. Derivatives of Inverse, Exponential, & Logarithmic Functions2h 37m
7. Antiderivatives & Indefinite Integrals1h 26m
8. Definite Integrals4h 44m
9. Graphical Applications of Integrals2h 27m
- Area Between Curves
  1h 18m
- Introduction to Volume & Disk Method
  1h 8m
10. Physics Applications of Integrals 3h 16m
- Kinematics
  1h 13m
- Work
  2h 3m
11. Integrals of Inverse, Exponential, & Logarithmic Functions2h 34m
12. Techniques of Integration7h 39m
13. Intro to Differential Equations2h 55m
14. Sequences & Series5h 36m
15. Power Series2h 19m
- Introduction to Power Series
  1h 9m
- Taylor Series & Taylor Polynomials
  1h 10m
16. Parametric Equations & Polar Coordinates7h 58m

7. Antiderivatives & Indefinite Integrals

Antiderivatives

Calculus

7. Antiderivatives & Indefinite Integrals

Antiderivatives

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Multiple Choice

Which of the following is an antiderivative of $\cos x$ ?

\sin x + C

\cos x + C

- \cos x + C

- \sin x + C

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Verified step by step guidance

Understand the problem: We are tasked with finding an antiderivative of cos(x). An antiderivative is a function whose derivative gives back the original function. In this case, we need a function whose derivative is cos(x).

Recall the derivative rule for sine and cosine: The derivative of sin(x) is cos(x), and the derivative of -cos(x) is sin(x). This will help us identify the correct antiderivative.

Apply the antiderivative concept: Since the derivative of sin(x) is cos(x), the antiderivative of cos(x) is sin(x). Additionally, we add a constant of integration, C, because the derivative of any constant is zero.

Compare the options: The correct antiderivative of cos(x) is sin(x) + C. The other options, such as cos(x) + C, -cos(x) + C, and -sin(x) + C, do not satisfy the condition that their derivative equals cos(x).

Conclude: The correct answer is sin(x) + C, as it is the function whose derivative is cos(x).