MAT 296 Calc2 Exam 1

Washer/Disk equation

Tube/Shell equation

y = ax

y = ax + b

y = x² + ax

y = -x² + ax

y = x² +or- a

y = +or- a - x²

y = x^p

arc length

SA length

y = f(x)

integration by parts formula

LIPET(order of what to use as f for integration by parts)

Log, Inverse trig, Polynomial, Exp function, trig function

Integral of ln(x)

= xlnx - x +C

sin²x + cos²x =

1

1 - sin²x =

cos²x

1 - cos²x =

sin²x

(even powers)sin²x =

½ - ½ cos2x

(even powers)cos²x =

½ + ½ cos2x

First Day Shortcut

tan²x +1 =

sec²x

sec²x - 1 =

tan²x

When the power of tan is odd

move a sec x tan x and u = sec x

When the power of sec is even

move a sec²x and u = tan x

When the power of sec is even and tan is odd

either will work

Integral of: sec x dx =

ln|secx + tanx| + C

Integral of: sec²x dx =

tanx + C

Integral of: tan x dx =

-ln|cosx| + C

Integral of: tan²x dx =

tanx - x + C

Integral of: tan³x dx =

tan²x / 2 + ln|cosx| + C