This chapter discusses integration, including defining indefinite integrals, evaluating definite integrals, and techniques for integration. The key topics covered include:
- Defining antiderivatives and indefinite integrals, and using properties like ∫(f(x))' dx = f(x)
- Evaluating definite integrals using properties like the Fundamental Theorem of Integral Calculus
- Integration techniques like using substitution, integration by parts, and trigonometric substitutions
- Applying integrals to real-world applications like finding the area under a curve, consumers' and producers' surplus, and cost functions
An antiderivative of a function is a function whose derivative is the given function. The problem of antidifferentiation is interesting, complicated, and useful, especially when discussing motion.
This is the slideshow version from class.
An antiderivative of a function is a function whose derivative is the given function. The problem of antidifferentiation is interesting, complicated, and useful, especially when discussing motion.
This is the slideshow version from class.
Lesson 8: Derivatives of Polynomials and Exponential functionsMatthew Leingang
Some of the most famous rules of the calculus of derivatives: the power rule, the sum rule, the constant multiple rule, and the number e defined so that e^x is its own derivative!
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