Mac2312 - Study guides, Class notes & Summaries

Integration By Parts uv - ∫ v du, u = LIPET ∫ sin^m(x)cos^n(x) dx n or m is odd u-sub ∫ sin^m(x)cos^n(x) dx n and m is even half-angle formula sin^2(x) (1 - cos2x) / 2 cos^2(x) (1 + cos2x) / 2 ∫ tan^m(x)sec^n(x) dx m and n are even save pair sec(x)tan(x)

∫1/(a^2 + x^2)dx(1/a)arctan(x/a) Horizontal Tangent Linesdy/dt = 0, dx/dt /= 0 cos^2(x) (half angle)½(1+cos2x) How do you find the equation of a tangent line?Find slope, find point, plug into (y - a) = m (x - b) Vertical Tangent Linesdy/dt /= 0, dx/dt = 0 sinxcosx

What is the formula for integration by parts? Integral of udv = uv - integral of vdu What is typically the best choice for U? Log, inverse trig What is typically the best choice for DV? Trig, exponential What is the priority list for by parts? LIATE What does L in LIATE mean? Log What does I in LIATE mean? Inverse trig What does A in LIATE mean? Algebraic

∫1/(a^2 + x^2)dx(1/a)arctan(x/a) Horizontal Tangent Linesdy/dt = 0, dx/dt /= 0 cos^2(x) (half angle)½(1+cos2x) How do you find the equation of a tangent line?Find slope, find point, plug into (y - a) = m (x - b) Vertical Tangent Linesdy/dt /= 0, dx/dt = 0 sinxcosx How to determine Tangent Line when dy/dt = 0, dx/dt = 0lim t->n (dy/dt)/(dx/dt)

Integration By Parts uv - ∫ v du, u = LIPET ∫ sin^m(x)cos^n(x) dx n or m is odd u-sub ∫ sin^m(x)cos^n(x) dx n and m is even half-angle formula sin^2(x) (1 - cos2x) / 2 cos^2(x) (1 + cos2x) / 2 ∫ tan^m(x)sec^n(x) dx m and n are even save pair sec(x)tan(x)

What is the formula for integration by parts? Integral of udv = uv - integral of vdu What is typically the best choice for U? Log, inverse trig What is typically the best choice for DV? Trig, exponential What is the priority list for by parts? LIATE What does L in LIATE mean? Log What does I in LIATE mean? Inverse trig What does A in LIATE mean? Algebraic

These notes go over the definition and examples for Shell Method, Arc Length and Surface Area. You will see drawings and annotations from examples that will be useful for your homework and exam. There is also on example in which you have to utilize disk/washer method.

In-class notes and examples regarding Washer, Disk, and the General Slicing method. The shapes in the examples include cylinders, parabolic cubes and revolving around a certain region.

These in-class notes go over the FTC, Mean Value Theorem, and definite integrals. It includes lots of examples and steps to get to the the answers. These notes also touch base on even and odd functions.