MATH 203 Spring 2007

TEST 3

8 problems, 10 points each

Instructions:

1. Show enough work to justify your answers

2. Write the problems in the given order.

3. Start each problem on a new page.

4. Don't leave blank pages.

  1. Evaluate the integral: MATH
    MATH

  2. Find all antiderivatives of the following function: $f(x)=e^{-x}.$

  3. Evaluate the integral by substitution MATH.
    MATH

  4. Find the antiderivative $F$ of the function $f(x)=3x^{2}-1$ satisfying the initial condition $F(1)=0.$

  5. Simplify and evaluate the integral MATH
    MATH

  6. Provide the formula of the Riemann sum (don't evaluate it) for the integral MATH, where function $f(x)\ $is plotted below, with $n=6$ intervals$,$ and with the left ends chosen as the representative points$.$ Provide an illustration below of the terms of the Riemann sum.
    MATH
    $.$

  7. Evaluate the definite integral MATH
    MATH

  8. Suppose the speed of a car was changing continuously following the rule $60-t^{2}$ per hour, where $t$ is the number of hours passed since noon. Find the average speed of the car between 1 pm and 3 pm.

This document created by Scientific WorkPlace 4.1.