Calc 2 Final

∫e^xdx

e^x + C

∫sinxdx

-cosx+c

∫sec²xdx

tanx+c

∫secxtanxdx

secx+c

∫1/x²+1

arctan(x)+c

∫1/xdx

ln|x|+c

∫a^x dx

a^x/lna + C

∫cosxdx

sinx+c

∫csc²xdx

-cotx+C

∫cscxcotxdx

-cscx+c

∫1/√1+x²dx

arcsinx+C

Fundamental theorem of calculus?

∫ from a to b, f(x)dx=f(b)-f(a)

∫tanxdx

ln|secx|+c

∫cotxdx

-ln|cscx|+c

secx

1/cosx

e^ln(x)

x

sin(pi/2)

1

ln(e)

1

ln(1)

0

∫1/√x dx

(x^1/2)/1/2

Integration by parts formula?

∫udv= uv-∫vdu

ln(x)dx

1/x

Partial fractions method?

∫1/x²dx=∫A/x dx + ∫B/x dx

sin²x+cos²x=?

1

1-sin²x=?

cos²x

If the limit of an improper integral exists, it’s ___

convergent

If the limit of an improper integral DNE/infinity, it’s __

divergent

P series

∫ from 1 to infinity 1/x^p dx, if p>1 its convergent, if p<1 or p=1 its divergent

Split integral formula?

∫c to a f(x)dx = ∫b to a f(x)dx + ∫c to b f(x)dx

what does ln|0| approach?

infinity

arctan(infinity)=?

pi/2

What is a point of discontinuity

When the function is undefined (gap in the graph)

1/infinity = ?

0

Disk/Washer formula

V = ∫ from a to b (pi)R²(x)dx

Shell method formula?

V=2(pi)∫ from a to b R(x)h(x)d(x)

f(y)=?

x

when y=e^x, x=?

ln y

Riemann sum formula?

A=sum of (deltax)f(xi)

Delta x=?

b-a/n

Area between 2 curves formula?

A=∫from a to b [f(x)-g(x)]dx

Arc length formula?

L=∫from a to b √1+[f’(x)]²dx

Average of function?

Fave=(1/b-a)∫from a to b f(x)dx

Mean Value Theorem

f’c = f(b)-f(a)/(b-a)

sin(pi)=?

0

cos(pi)=?

-1