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Concepts of Integration

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Please solve the following integration application problems. Please provide steps to arrive at final answer.

1. Find the solid of revolution for f(x) = x^2 and g(x) = 1/2 x^3 for x∈[2, 3]
2. What are the coordinates of the centroid for f(x) = x ∀∈[0, 2]
3. Integrate x^2 + 3x - 4 / x
4. How much total work is expended over a 10-minute period if the force function is given by F(t) = 4t^3 - 6t^2 - 5t
5. If f(x) = x^2, find its solid volume for x∈[-3, -1]
6. Integrate 1 / (x^2 + 2x + 1)+1
7. What is the arc length of h(x) = x^0.5 for x∈[0, 5].

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Concepts of Integration are presented in the solution.

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