Applications of Integration Flashcards
1
Q
Formula for integrating top to bottom
A
A = ∫ ba (top - bottom) dx
2
Q
Formula for integrating right to left
A
A = ∫ ba (right - left) dy
3
Q
Area formula of isosceles w/ leg
A
A = 1/2 * b^2
4
Q
Area formula of isosceles w/ hypotenuse
A
A = 1/4 b^2
5
Q
Area formula for equilateral
A
A = (sqrt 3) / 4 *b^2
6
Q
Area formula for a semicircle
A
A = 1/8 * pi * b^2
7
Q
Arc length formula
A
∫ sqrt ( 1 + (dy/dx)^2 ) dx
OR
∫ sqrt ( 1 + (dx/dy)^2 ) dy
8
Q
If it is perpendicular to…
A
x-axis: use dx
y-axis: use dy
9
Q
Steps to integrating slices
A
1) Draw a sketch (or look at graph)
2) Are your slices vertical or horizontal (dx or dy)
3) Write a slice in terms of b and plug into equation.
10
Q
For arc length with a flat line…
A
Don’t forget to find the distance of it as well!
11
Q
For a revolved solid, do..
A
Outer - inner
R - r
