022 Exam 2 Sample B, Problem 6

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Find the area under the curve of  between the -axis and .

Foundations:  
For solving the problem, we only require the use of the power rule for integration:
For setup of the problem we need to integrate the region between the x - axis, the curve, x = 0 (the y-axis), and x = 4.

 Solution:

Step 1:  
Set up the integral:
Step 2:  
Using the power rule we have:
Step 3:  
Now we need to evaluate to get:
Final Answer:  

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