calc 2b midterm 2

∫cos(x)

sin(x)+c

∫sin(x)

-cos(x) +c

∫sec²(x)

tan(x)+c

∫csc²(x)

-cot(x)+c

∫sec(x)tan(x)

sec(x)+c

∫csc(x)cot(x)

-csc(x)+c

∫x/1

ln/x/ +c

∫e^x

e^x+c

∫b^x

(1/ln(B)) (b^x) +c

∫1/√(1-x²)

sin-1(x) +c

∫1/(1+x²)

tan-1(x) +c

∫1/x√(x²-1)

sec-1(x) +c

area of a trapazoid

(b1+b2)/2 x h

area of half circle

½ pi r²

definite intergral

∫ba f(x)dx= lim n→infiniti ∑nk=1 f(xk)Δx

∑nk=1 k

n(n+1)/2

1/sin(θ)

csc(θ)

1/cos(θ)

sec(θ)

1/tan(θ)

cot(θ)

1/csc(θ)

sin(θ)

1/sec(θ)

cos(θ)

1/cot(θ)

tan(θ)

sin²(θ) + cos²(θ)=

1

tan²(θ) + 1=

sec²(θ)

1 + cot²(θ)=

csc²(θ)

integration by parts formula

∫udv= uv - ∫uvdu

how to determine which is u and which is dv- D E T A I L

d exponential trig algebraic inverse trig log

dv ← →u

√1-x²

x=sin(θ)

√1-sin²(θ) = cos(θ)

√1+x²

x=tan(θ)

√1-tan²(θ) = sec(θ)

√x²-1

x=sec(θ)

√sec²(θ)-1 = tan(θ)

case 1: odd number of cos

u= sin (x)

du= cos(x)dx

case 2: odd number of sines

u=cos (x)

du= -sin(x)

case 3: odd number of tangents or cotangents

u= sec(x)

du= sec(x)tan(x)

or

u=csc(x)

du= -csc(x)cot(x)

case 4: even number of secants or cosecants

u= tan(x)

du= sec²(x)

or

u=cot(x)

du= -csc²(x)

case 5: even number of sines or cosines

half angle identities