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AB/Basic Integration
Today we reviewed the AB integration rules. I need to memorize the inverse trig formulas. I need to remember when to use shell method and when to use disk method. Disk method integrates (pi)(r^2) and shell method integrates 2(pi)(r). If i graph the function and draw the rectangle I can visualize how to integrate it best. -
Infinite Series Review
Important series to remember/recognize: geometric and power series. We can find the sum for series that are geometric and alternating (most of the time). Always use nth term test first. Ratio test is second best bet if the series does not appear to be geometric, power, alternating,or telescopic. If test resembles a well known series then use DC test. Use root test if there is an X in the exponent. Root and ratio test follow the same pattern that a limit under 1 means convergence, limit over one -
Taylor Polynomials and remainders
Taylor polynomials are great!!! learn to recognize the important Maclaurian ones (e^x, sinx, cosx, 1/x, lnx, etc.). If all else fails and you have to generate a taylor by scratch, write out the derrivatives of the power given, and construct the taylor polynimial. If you have an alternating series you are in luck!!! the max error is the next term. Use lagrange if it's not alternating. -
Differential Equations
Always show separating variables- the AP graders give a point for that. Dont forget that the "+c" gets becomes Ce^u because of log rules. in a logistic growth population equation, make sure to leave the constant on the x side, and us partial fractions to tackle the y side. It will be time efficient to memorize which number in the rate equation is the carrying capacity. -
Advanced Integration
Memorize the integration by parts formula-it has a nice ring to it! Don't forget to use LIPET when chosing the U. Tabular method is great, use in place of IBP as long as u and dv are not infinitely differentiable. Don't bother using trig subsitution on the test, it is too time consuming. Partial fractions are also useful, use in case of a factroable, polynomail denominator of a larger power than numerator. -
Application of Integrals
Arc length formula is the square root one plus f rpime squared. Surface area.
