Exam 4 review: Integrals

\int cot(x) dx

ln|sin(x)| + C

\int csc(x) dx

-ln|csc(x) + cot(x)| + C

Determinate or indeterminate?

infinity * 0

Indeterminate

Determinate or indeterminate?

1^infinity

indeterminate

Determinate or indeterminate?

infinity - infinity

Indeterminate

Determinate or indeterminate?

Infinity * infinity

Determinate

Determinate or indeterminate?

infinity^infinity

Determinate

Determinate or indeterminate?

infinity + infinity

Determinate

Determinate or indeterminate?

small number^small number (0^0)

Indeterminate

Determinate or indeterminate?

0/0

Indeterminate

Determinate or indeterminate?

Infinity/infinity

Indeterminate

Determinate or indeterminate?

Infinity^0

Indeterminate

\int 1/(1 + x²)dx

arctan(x) + C

\int w^4dx (notice it’s dx)

w^4*x + C

\int tan(x) dx

-ln|cos(x)| + C

\int a^x dx

a^x / ln|a| + C

\int\frac{1}{\sqrt{1-x^2}}dx

arcsin(x) + C

\int\frac{1}{1+x^2}dx

arctan(x) + C

\int\frac{1}{\vert x\vert\sqrt{x^2-1}}dx

arcsec(x) + C

-\frac{1}{\sqrt{1-x^2}}+C

arccos(x) + C

Left endpoint sum

xi* = a + (i - 1)(change in x)

Change in x

(b-a)/n

Right endpoint sum

xi* = a + i(change in x)

MVT (average value)

(1/b-a)integral f(x)dx