Find the indefinite integral and check your result by differentiation. ∫5 x^-3 d x

Name: Problem 13, Chapter 5: Calculus an Applied Approach
Uploaded: 2021-06-11T15:50:34-08:00
Duration: 2 min 10 s
Channel: Yaw Asomani
Description: Find the indefinite integral and check your result by differentiation. ∫5 x^-3 d x

step 1 Things are getting a little more interesting as we go forward, which is a pretty good thing. And

Find the indefinite integral and check your result by...

Key Concepts

Indefinite Integration

Indefinite integration is the process of finding the most general antiderivative of a function. Unlike definite integration, which yields a numerical value, indefinite integration results in a family of functions that differ by an arbitrary constant, and it expresses the antiderivatives of the original function.

Power Rule for Integration

The power rule for integration is a fundamental technique used to integrate functions of the form x^n. This rule states that ? x^n dx = x^(n+1)/(n+1) + C for all real numbers n except -1. It provides a straightforward method of finding antiderivatives for power functions by incrementing the exponent and dividing by the new exponent.

Constant of Integration

The constant of integration, typically represented by C, is included in the result of an indefinite integral because the derivative of any constant is zero. This constant accounts for all possible vertical shifts that yield the same derivative, encapsulating the family of antiderivatives.

Differentiation as a Verification Tool

Differentiation is used as a method to verify the correctness of an integration result. By taking the derivative of the antiderivative, one should obtain the original function, ensuring that the integration process was performed correctly. This technique helps in confirming the validity of the obtained solution.

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