Question

Evaluate the integrals. $$ \int \sqrt[4]{x} d x $$

   Evaluate the integrals.
$$
\int \sqrt[4]{x} d x
$$

Finite Mathematics and Applied Calculus

Finite Mathematics and Applied Calculus

Stefan Waner, Steven… 5th Edition

Chapter 13, Problem 17

Instant Answer

Solved by Expert Rukhmani Jain

10/01/2021

Step 1

This can be rewritten as $\int x^{1/4} dx$. Show more…

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Evaluate the integrals. $$ \int \sqrt[4]{x} d x $$

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Key Concepts

Fractional Exponents

Fractional exponents allow roots to be expressed as exponents, converting radical expressions into a form that is easier to manipulate algebraically. By rewriting a radical, such as the fourth root of x, as x^(1/4), one can straightforwardly apply the power rule for integration and other calculus-based operations.

Power Rule for Integration

The power rule for integration is a basic technique used for finding antiderivatives of functions in the form x^n, where n is any real number except -1. According to this rule, the antiderivative of x^n is given by (x^(n+1))/(n+1) + C. This method is essential for handling polynomial functions and those expressed with fractional exponents.

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