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Arts & Science MATH 116 CALCULUS II

Midterm 1 (50 marks available)

Feburary 10, 2016

1. Evaluate the sum:

2. Use the definition of the definite integral as a limit of a Riemann sum to evaluate the area under the graph of f (x) = x 2 - 1 in the first quadrant between x = 1 and x = 3. You must take sample points to be the right endpoint of each subinterval. Here are some useful summation formulae:

3. Use Part 1 of the Fundamental Theorem of Calculus to find g'(0) if

4. The velocity function (in meters per second) for a particle moving along a straight line is

5. Evaluate the integral dx by interpreting it in terms of areas.

6. Evalutate the integrals:

(a)

(b)

(c)

(d) In(sin x)cot x dx

7. Find the area of the region R bounded by the curves y2 = 3 - x and x = 2y.

8. Consider the region R in the first quadrant of the plane bounded by the curves x = 0, and y = 0.

(a) Use the disk/washer method to find the volume of the solid obtained by rotating the region R about the line y = -1.

(b) Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region R about the line x = 4 .