Math 220-2 Practice

d/dx(sin(x))

cos(x)

d/dx(cos(x))

-sin(x)

d/dx(tan(x))

sec^2 (x)

d/dx(sec(x))

sec(x)tan(x)

d/dx(cot(x))

-csc^2 (x)

d/dx(csc(x))

-csc(x)cot(x)

d/dx(b^x)

b^x ln(b)

d/dx(e^x)

e^x

d/dx(e^-x)

-e^-x

d/dx(arcsin(x))

1/(1-x^2)^1/2

d/dx(arccos(x))

-1/(1-x^2)^1/2

d/dx(arctan(x))

1/(1+x^2)

d/dx(arccot(x))

-1/(1+x^2)

d/dx(arcsec(x))

1/x(x^2 - 1)^1/2

d/dx(arccsc(x))

-1/x(x^2 - 1)^1/2

d/dx[log(base b)x]

1/xln(b)

d/dx(lnx)

1/x

d/dx(ln|x|)

1/x

Area between Curves ∫

∫f(x)-g(x)dx

Disk Method π

π∫(f(x))²dx

Washer Method π∫

π∫R² - r² dx

∫sinxdx

-cos(x) + c

∫cosxdx

sin(x) + c

∫ tanxdx

-ln|cos(x)|+c

∫cotxdx

ln|sinx|+c

∫secxdx

ln|sec(x)+tan(x)| + c

∫ cscxdx

-ln|cscx+cotx| + c

∫sec^2 x dx

tan(x) + c

∫csc^2 x dx

-cot(x)+c

∫secxtanx

sec(x) + c

∫csc(x) cot(x) dx

-csc(x) + c

∫1/(a^2 - x^2)^1/2 dx

arcsin(x/a) + c

∫1/(a^2 + x^2) dx

(1/a)arctan(x/a) + c

∫ 1/(x(x^2 - a^2)^1/2

1/a arcsec(|x|/a) + c

Displacement

∫v(t) dt

Total Distance Traveled

∫|v(t)|

∫x^n dx

((x^ (n+1))/(n + 1)) + C

∫1/x dx

ln|x| + c

∫e^x dx

e^x + c

∫b^x dx

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

Integration by parts ∫

∫udv = uv - ∫vdu

LIATE for finding U in integration by parts

Logs, inverse, algebraic, trig, exponential