Math Problem Statement
Complete the table with the integral \( \int 8 \sqrt{x} \, dx \). Rewrite the integral, integrate it, and simplify.
Solution
The integral provided is:
Let's complete each section of the table step by step.
1. Rewrite the Original Integral:
The square root of can be written as a fractional exponent:
2. Integrate:
To integrate , we apply the power rule for integration, which states:
For , this gives:
Simplify the fraction:
3. Simplify:
The simplified
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Math Problem Analysis
Mathematical Concepts
Integration
Exponents
Formulas
Power Rule for Integration: \( \int x^n \, dx = \frac{x^{n+1}}{n+1} + C \)
Theorems
-
Suitable Grade Level
Grades 11-12
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