Calc 2 Exam 1

integration by parts formula

∫udv = uv - v∫du

∫sinxdx =

-cosx + C

∫cosxdx =

sinx + C

∫tanxdx =

-ln|cosx| + C

∫cotxdx =

ln|sinx| + C

∫secxdx =

ln|secx+tanx| + C

∫cscxdx =

-ln|cscx+cotx| + C

sin²x + cos²x =

1

half angle identity: cos²x =

1/2(1+cos(2x))

half angle identity: sin²x =

1/2(1-cos(2x))

∫secxdx =

ln|secx+tanx| + C

∫sec³xdx =

1/2(secxtanx + ln|secx + tanx|) + C

cot²x + 1 = csc²x

a² - u²

u=asinθ; 1-sin²θ = cos²θ

u² + a²

u=atanθ ; tan²θ + 1 = sec²θ

u² - a²

u = asecθ ; sec²θ - 1 = tan²θ

$$\frac{∫dx}{a^2+x^2}=\frac{1}{a}\arctan\left(\frac{x}{a}\right)+C$$

Area of a Circle

A=πr²

Area of a Semi Circle

$$A=\frac{\pi r^2}{2}$$

LIPET

Logarithms, Inverse trig functions, Polynomials, Exponentials, Trigonmetric functions

For PFD: when do you do long division?

when the degree in the denominator is greater than the degree in the numerator

y=x²

y=sinx

y=cosx

y=x³

y=2x-4x²

$$y=\sqrt{x}$$

y=lnx

y=e^x