MEMORIZE THESE EQUATIONS- AP CALC AB

basic Integral/Area and Solids of Revolution/writing limits of Riemann sums as integrals/Equations for cross sections

What is integral for 1/u times du , if u=ax^1+b?

1/u’ times ln|u|+c

integral for

cos x

-sinx

sec²x

-csc 2x

ans:

sinx +c

cosx+c

tanx+c

cotx+c

how cam you rewrite the integral for x/4dx

¼ times integral for xdx

integral 1/xtimes dx

ln|x|+c

integral a^u du

a^u/lna. +c

intergal tan udu

-ln|cosu+c|

area between two curves perp to x axis or y axis

integral from a to b for (f(X)-g(x))dx

volume by disk methods about x-axis or y-axis

pi times the integral from a to b for (R(x))²dx

Volume by washer method about x-axis and y-axis

pi times the integral from a to b for ((R(x)²-r(x)²)dx

Volume by shell method:

2 pi times the integral from a to b for (R(x))dx

Cross section for squares:volume

v=integral from a to b (base)²dx

equilateral triangle cross section

v=rad ¾ times the integral from a to b (base)²dx

isosceles right triangle cross section

v= 1/4 times the integral from a to b (base)²dx

cross section rectangles

v= integral from a to b (base times h)dx

cross sections semi circles

v= pi/2 times integral from a to b (radius)²dx