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MATH 2B - Summer I 2025

Practice Midterm

2. No work required

(a) (2 points) Write  x2 ln x dr using the limit definition of the integral. (Don't evaluate the limit).

(b) (2 points) Let v(t) = t2 - 9 for 1 ≤ t ≤ 4. Write an integral expression for the net change in displacement. Then write the integral for the total distance traveled.

(c) (2 points) If  f(x) dr = 20,  f(x) dx = 6 and  g(x) dr =-4. Find

(d) (2 points) What is the upper bound of integration in 

(e) (2 points) If you were going to apply the substitution rule to the following integral

what is the best candidate for u?

3. (10 points) Let

Find F'(x).

4. (10 points) Approximate the area under f(z) =  on [1,5] using the right endpoint rule with 4 rectangles.

5. (20 points) Evaluate

6. (20 points) Evaluate

7. (20 points) Compute

8. (a) (10 points) Find the area between y = x3 and y =

(b) (10 points) Find the volume generated by rotating this region around the y-axis.

(c) (10 points) Find the volume generated by rotating this region around the z-axis.

9. (20 points) Evaluate