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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/area

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 following equation represents what math term?

\intf(x)\ dx

Indefinite Integral

200

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

k\ \int \ f(x)\ dx

200

This is how to find the width of each rectangle in a Riemann Sum. 

What is (b-a)/n

200

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

-2

200

\int\ 2sin(x)\ dx

-2cos(x)+C

300

This term is an approximation of Left and Right Endpoint Rectangles in order to find the area of an irregular region.

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

Reimann Sums

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

What value must you always add to your indefinite integral answer?

A constant term. 

400

\int\ 4x^3+2x\ dx=

x^4+x^2+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

What is the starting value of whatever you have in a problem called?

An initial value. 

500

\int\ x^.5+3x^2\ dx=

2(x^1.5)/3 +x^3/3+C

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

Which of the 50 states has the longest coastline?

Alaska

500

\int 2/\sqrt x\ dx=

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