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Vocabulary
Basic Integration Rules
Riemann Sums
Definite Integrals
Indefinite Integrals
100
This term is a synonym for an integral.
What is an Anti-derivative?
100

\int\ k\ dx=

kx+C

100
The primary use of Riemann sums is to find this
What is area under a curve?
100

\int_0^2\ 6x\ dx=


12

100

\int\ 3x^2\ dx

x^3+C

200

The equation following equation represents what math term?

\intf(x)\ dx

Indefinite Integral

200

\int\ k\ f(x)\ dx=

k\ \int \ f(x)\ dx

200
This type of Reimann Sum uses both triangles and trapezoids in its approximation
What is a Trapezoidal Riemann Sum?
200

\int_-1^0\ 2x-1\ dx

-2

200

\int\ 2sin(x)\ dx

-2cos(x)+C

300

This term is an approximation that takes the following form:

lim_(n\to\oo)\Sigma_(k=1)^n\ f(x_k)\ \Deltax

Riemann Sum

300

\int\ cos(x)\ dx=

sin(x)+C

300
This Riemann sum uses rectangles with length determined from the right side of a curve.
What is a Right Riemann Sum?
300

\int_-1^1\ t^2 - 2\ dt

-10/3=-3.\bar3=-3\ 1/3 

300

\int\ 1/(x^3) \ dx

-1/(2x^2) +C

400

This theorem states "If 'f' is continuous on the closed interval [a,b], there exists a number 'c' in the closed interval [a,b] such that

\int_a^bf(x)\ dx=f(c)(b-a)

The Mean Value Theorem (for Integrals)

400

\int\ sec(x)tan(x)\ dx=

sec(x)+C

400
This Riemann sum uses rectangles with length determined from the left side of a curve.
What is a Left Riemann Sum?
400

\int_0^n\ 1+sin(x) \ dx

n-cos(n)+1

400

\int\ 4x^3 - 10x - 3\ dx

x^4 - 5x^2 - 3x + C

500

The value of f(c) given in the Mean Value Theorem for Integrals is called this:

The Average Value of a Function (on that integral)

500

\int\ csc(x)cot(x)\ dx=

-csc(x)+C

500
The name Riemann sum comes from the name of this German mathematician.
Who is Bernhard Riemann or Georg Riemann?
500

\int_0^4\ |x^2-9| \ dx

64/3

500

\int 2/\sqrt x\ dx=

4x^(1/2) + C=4\sqrt x +C