Test 4: Concept Review

Section 4.10:

• Finding general anti-derivatives
• Finding specific anti-derivatives
• Differential equations
• Direction Fields

Section 5.1:

• Area as a limit of rectangles
• sample points
• sigma notation
• left and right endpoint rectangle approximations
• the ``dirt'' formula (distance = rate time)

Section 5.2:

• Definition of a definite integral
• Riemann sum
• vocabulary (integrand, integral sign, differential, limits of integration)
• midpoint rule
• trapezoidal rule (actually equivalent to the average of left and right rectangle rules)
• properties of the integral (1-8, pp. 331-333)

Section 5.3:

• Fundamental theorem of calculus
• graphing anti-derivatives from integrals

Section 5.4:

• Indefinite integrals
• Difference between definite and indefinite integrals
• Watch the continuity of the integrand (e.g. top of p. 348)
• Total Change theorem

Section 5.5:

• Substitution rule (using the chain rule in reverse)
• Difference between substitution for indefinite integrals and definite integrals (in which the limits of integration must be carefully handled!).
• Using symmetry to calculate integrals

Section 6.1:

• Areas between curves (making sure which function is on top of the other!)

Don't forget the basics from previous tests. While the focus will be on the new material, you will still be expected to be able to use the old!