You should be able to:

• Explain what is meant by an antiderivative of the function . (Section 6.1)
• Compute all possible antiderivatives for a given function (Section 6.1)
  • Compute a particular antiderivative F(x) given F(a) = b. (Section 6.1, see problems 41-47)
• Explain what is the indefinite integral of given function (Section 6.1)
  • Properties of the indefinite integral:
    • (Section 6.1)
• Compute the indefinite integral of various functions including (this is not an exhaustive list):
  • , where
  • exponential functions of the form
• Compute a definite integral using substitution (Section 9.1)
• You should be able to compute the definite integral for various functions. (Section 6.1)
  • You should know how interpret displacement in the context of a definite integral (Section 6.2, see example 6 and problem 31 and 33)
• Explain the geometric interpretation of the definite integral when . (Answer: The area under the graph of .) (Section 6.3)
• Compute the Riemann Sum of a function in order to approximate the area under the graph of a function. (Section 6.3)
  • Using left endpoints
  • Using right endpoints
• Compute area of the region bounded between the graph of a function and the -axis. (Section 6.4)

For Test 3 you should be able to:

• Solve an optimization problem (lots of good exercises from Section 2.5).
  • Remember you will be asked to sketch the graph of the objective function here!
• Use the product rule and chain rule (see Section 3.1 and Section 3.2).
• Sketch the graph of a function that satisfies the following properties:
  • for all in the interval
  • Section 4.2 may be a good reference for this material.
• Compute the derivative of functions that involve the exponential function. (Section 4.3)
• Recognize the exponential function as the solution to differential equation: . (Section 4.3)
• Draw the slope-field for a differential equation (See class notes)
• Solve simple equations involving logarithms and exponential functions. Remember these functions kill each other! (Section 4.4)
• Compute the derivative of functions that involve the natural logarithm (Section 4.5)
  • Use properties of logarithms to compute derivatives (Section 4.6)
• Use the exponential function in population and decay models (Section 5.1)
  • You may be asked to find the equation of a tangent line!