1.

Which of the following sums does not equal the others? (4 points)

2.

Estimate the area under the curve f(x) = x^{2} from x = 1 to x = 5 by using four inscribed (under the curve) rectangles. Answer to the nearest integer. (4 points)

3.

List x_{1}, x_{2}, x_{3}, x_{4} where x_{i} is the right endpoint of the four equal intervals used to estimate the area under the curve of f(x) between x = 3 and x = 5. (4 points)

4.

Write the summation to estimate the area under the curve y = 2x^{2} + 1 from x = 0 to x = 4 using 4 rectangles and left endpoints. (4 points)

5.

If the area under the curve of f(x) = x^{2} + 2 from x = 1 to x = 6 is estimated using five approximating rectangles and right endpoints, will the estimate be an underestimate or overestimate? (4 points)

1.

The Riemann sum, , is equivalent to with .

Write the integral that produces the same value as . (4 points)

2.

Write the Riemann sum to find the area under the graph of the function f(x) = x^{3} from x = 2 to x = 5. (4 points)

3.

Use your calculator to evaluate . Give your answer to the nearest integer. (4 points)

4.

Use geometry to evaluate . (4 points)

5.

Use geometry to evaluate . (4 points)

1.

Given that the antiderivative of is F(x) = Ln|x| + C, evaluate . (4 points)

2.

Evaluate . (4 points)

3.

Given , find G ‘(x). (4 points)

4.

Find . (4 points)

5.

Determine the interval on which f(x) = ln(x) is integrable. (4 points)