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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.

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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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