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Calculus Functions to Evaluate an Integral

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Please help with various Calculus questions.

You do not need to show your work for this one because I would simply like to compare your answers with mine so that I am sure that I did everything correct on mine. Please just write your exact answer after each number. I will know which problems I will have to study in detail with your help. Thank you very much.

Please double check all of your answers to that you are sure everything is correct. Thanks.

1. Evaluate the integral: .
2. Evaluate the integral: .
3. Evaluate the integral: .
4. Evaluate the integral: .
5. Find the particular solution of the equation that satisfies the condition f(1) = 12.
6. Use the properties of sigma notation and the summation formulas to evaluate the given sum:
7. Write the definite integral for the area of the region bounded by the graphs of and y = 0.
8. Evaluate the integral: .
9. Evaluate the integral: .
10. Calculate the area of the region bounded by the x-axis and the function .
11. Evaluate the integral: .
12. Evaluate the integral: .

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A calculus functions to evaluate an integral is given. The area of the regions bounded by the x-axis and the function is determined.

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