memorize for test

Volume of a Cylinder

pir²h

Area of a Cylinder

2pirh+2pir²

Antideriv of cosx

sinx+c

Anti deriv of sec²x

Tanx+C

Antideriv of sin

-cosx+c

Antideriv of secxtanx

secx+c

Antideriv of csc²x

-cotx+c

Antideriv of cscxcotx

-cscx+c

Volume of box

x²y

Area of box

2x²+4xy

Distance formula

r*t

V of rectangle

lwh

Riemann Sum?

xi=a+ideltax, deltax=(b-a)/n, f(xi), lim=f(xi)deltax

i

n(n+1)/2

i²

n(n+1)(2n+1)/6

i³

n²(n+1)²/4

abs valu

A=1/2bh

Sqrt something -x²

A=pir²

Trapezoid

A=(1/2)(b1+b2)h

Fundamental theorem of calc

F(h(x))h’(x)-f(g(x))g’(x)

X=

Right-left

Y=

Top-bottom

Cavaleri principal

A(x)dx

Prove volume right circular cone

0 to h pi(rx/h)²

Prove Volume of pyramid

0 to h (l1 x w1dx)=(lx/h)(wx/h)dx

Volume Rotated around region

pi(f(x))²dx

Washer method (two functions)

pi(rout)²-(ri)²dx

Shell

2pixf(x)dx

Arc length

sqrt(1+(f(x))²)dx

Proof volume of sphere by rotation

X²+y²=r², solve for y, 2 pisqrt(r²-x²)²dx

Proof of sa of sphere

2 2pi(rad)(arc)dx=2 2pi (sqrt(r²-x²))(sqrt(1+x²/r²-x²))dx

Surface area x-axis

2pi(rad)(arc)dx

Sa y axis

2pi(x)(arc)dx