Mathematics 134 – Intensive Calculus for Science 2 Exam I – February 17, 2006

Directions. Do all work in the blue exam booklet. You may use a calculator on any of the following problems. There are 100 possible points.

I. The given graph shows y = f(x).

A) (10) Use the graph to determine ∫_{0}^{4} f(x) dx. B) (5) Let F (x) be the antiderivative of f(x) with F (0) = −2. What is F (4)? C) (15) Give a qualitative sketch of y = F (x) from part B. Your graph should show where

F is increasing/decreasing, and where F is concave up/concave down. D) (5) The function G(x) is G(x) = ∫_{0}^{x} f(t) dt using the function f in the graph above.

What is G′(2)?

II. On the Moon, the acceleration due to gravity is about -1.6 m/sec^{2} (versus about -9.8 m/sec^{2} on Earth).

A) (10) A rock is tossed upward with initial velocity v(0) = 1 m/sec. Solve the equation

\frac{dv}{dt} = −1.6 to find the velocity of the ball as a function of time. B) (10) Use your answer v(t) from part A. If the rock’s initial height is h(0) = 1 m, solve

the equation \frac{dh}{dt} = v(t) to find the height of the rock as a function of time. C) (10) How long does the rock take to fall back to ground level on the Moon? Would

the corresponding time be longer or shorter on the Earth?

III. Compute each of the integrals below using basic rules and/or substitution. You must show all work for full credit.

A) (10)

∫ 3x^{7} − \frac{4}{x^{3}} + 5\sqrt{x} + \frac{7}{x} dx

B) (15)

∫_{0}^{1} sin(πx) + cos(πx) dx

C) (10)

∫ xe^{5x^{2}+7} dx