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Volume of the solid obtained by rotating the region

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1. For each of the following integrals do the following:

(i) Explain in one sentence why the integral is an improper integral.
(ii) Decide whether the integral is convergent or divergent. Justify your answer.

Please see the attachment for the integrals.

2. Find the area of the region bounded by the curve y = 3x - x^2 and the x-axis. Include a sketch of the area.

3. Find the area of the region bounded by the curves y = 2 - x, y = x^2 and the line y = 0. Include a sketch of the area.

4. Evaluate the following indefinite integrals:

Please see the attachment for the integrals.

5. Find the volume of the solid obtained by rotating the region bounded by the curves y = SQRT(x), x = 2 and y = 0 about the x-axis.
Include a sketch of the region and a typical cross-section with a plane orthogonal to the x-axis.

In questions 2, 3 and 5, give the answers in exact form (not a decimal approximation).

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