post #17

Okay so almost everything we did this week was basically in preparation for the exam on tuesdayyy, so i'm just going to go over some things from the past as a review.

Some things that we just learned that are extremely easy form me are finding the volume and area of disks and washers. atleast i know i'll pass some portion of the exams, assuming ofcourse, that they're even on there.

Area between curves:
formula: bSa top equation-bottom equation

example: Find the area of the region enclosed by y=-4x^2+41x+94 and y=x-2 between x=1 and x=7.

1. draw a picture

2. subtract the two equations: (-4x^2+41x+94-(x-2)-don't square, it's not volumee!
(-4x^2+41x+94-(-x+2)

3.combine like terms and integrate: S(-4x^2+41x+94-(-x+2))
(-4/3)x^3+20x^2+96x

4. plug in 1 and 6 and subtract: (3584/3)-(344/3)= 1080



FORMULA FOR DISKS: pi S[r(x)]^2dx, this formula is almost exactly the same as when you are asked to find the area of a disk, however, while finding the area you do not square the radius (the given equation).

FORMULA FOR WASHERS: pi S[(top)^2-(bottom)^2]dx


TANGENT LINES!
Steps:
Take the first der...f ‘(x).
Plug in x to find your slope: m.
Plug x into original functiong..f(x) to find y (if not already given).
Using your slope..m and (x,y), plug it into slope-intercept form: (y-y1) = m(x-x1)



okayy something i don't understandd! umm i really don't get how to integrate a fraction, which would be integration by substitution i'm assumine. also some things from the past that would be nice to go over is ofcourse optimization, related rates type stuff. other than that, i think i'm okayy, maybe trapezoidal rule but that's about it! help would be WONDERFULL!