Area & Geometric Shapes
This is the Area of a Rectangle
What is base multiplied by height? (or length multiplied by width)
This is the collection of non-overlapping subintervals on the [a,b] interval that have a total length of b-a when combined together.
What is a partition?
The constant 1.
What is x+C?
\int_0^{1}1\cdot dx
What is 1?
d/dx(\int_a^x2t\cdot dt)
What is 2x?
This is the Area of a Triangle.
What is
1/2b\cdot h
The length of the longest partition width.
What is the partition norm?
The function
x
What is
1/2x^2 +C
\int_0^1x\cdot dx
What is
1/2
d/dx(\int_a^xcos(t)\cdotdt)
What is
cos(x)
This is the Area of a Circle.
What is
\pi \cdot r^2
S_n=\sum_{k=1}^nf(c_k)\cdot\Deltax_k
What is a Riemann Sum?
The function
x^2
What is
1/3x^3+C
\int_{-\pi}^{pi}sin(x)dx
What is 0?
\int_0^{2}2t\cdot dt
What is 4?
The integration of a constant c=1 over the [0,1] interval is this area.
What is \int_0^{1}1\cdotdx=1. ? This is the area of a rectangle.
A particular partition such that the width of all subintervals on [a,b] are of equal width.
What is a regular partition?
The function
1/x
What is
ln(x)?
\int_0^1x^2\cdot dx
What is
1/3
\int_0^{2}3t^2dt
What is 8?
The integration of f(x)=x over the interval [0,1] is this area.
What is
\int_0^1x\cdot dx=1/2. ?
This is the area of a triangle.
This symbol
\int
What is the Integral sign?
The function
e^x
What is
e^x
\int_1^e1/xdx
What is 1?
d/dx(\int_x^{a}2t\cdot dt)
What is
-2x