Guidelines for Exam 1 preparation

To be successful on Exam 1, you should

• be able to find the average value of a function over an interval.
• be able to find the area between two given curves, over a given interval.
• be able to find the area of a region bounded by two or more given curves, integrating with respect to x or with respect to y.
• be able to find the volume of simplee solids by integrating cross-sectional area.
• be able to find the volume of a solid, given the base of a solid (and placement) of a typical cross-section.
• be able to find volumes of solids of revolution using the disc/washer method and/or the method of cylindrical shells, when rotated about the x-axis, the y-axis, or other horizontal or vertical lines, integrating with respect to x and/or y.
• be able to find the mass of a region or a solid of the types described above, provided the density functions depends on only one variable.
• be able to evaluate anti-derivatives by changing variable via straightforward using "u-substitution."
• be able to evaluate anti-derivatives by changing variables, using "u-substitution with inversion."
• be able to evaluate anti-derivatives involving products of power functions, logarithms, trigonometric functions, exponential function, and/or inverse trigonometric functions using integration by parts.
• be able to use integration by parts and algebraic manipulation (the "I-trick") and/or setting dv=dx to find anti-derivatives.
• be able to find anti-derivatives of products of powers of trigonometric functions using trigonometric identities and "u-substitution," and algebric manipulation.
• be able to evaluate integrals involving sums or differences of squares using trigonometric substitution.
• be able to find partial fraction decompositions and anti-derivatives of rational functions whose denominators involve only linear factors (possibly repeated).

You will need to show all work in order to receive credit.