Exact Area Under the Curve
Riemann Sum Estimations
Random Trivia
Infinite Riemann Sum Notation
Definite Integral Notation
100
This is the exact area of the function's curve in relation to the x-axis on the closed interval [0, 12].
What is -6 Units?
100
This is the approximate area of the function's curve in relation to the x-axis using a Right-Hand Riemann Sum with 4 subintervals on the closed interval [-2, 2].
f(x)=3x^2+1
What is 22 Units?
100
This is Mrs. Addams first name in The Addams Family.
What is Morticia?
100
This is the Infinite Riemann Sum conversion of the definite integral
\int_2^5\sqrt(x)dx
What is
lim_(n\rightarrow\infty)\sum_(k=1)^n(3/n)\sqrt(2+(3k)/n)?
100
This is the definite integral conversion of the Infinite Riemann Sum
lim_(n\rightarrow\infty)\sum_(k=1)^n(3/n)((3k)/n)^4?
What is
\int_0^3 x^4dx?
200
This is the exact area of the function's curve in relation to the x-axis on the closed interval [-2, 4].
What is 7 Units?
200
This is the approximate area of the function's curve in relation to the x-axis using a Left-Hand Riemann Sum with 6 subintervals on the closed interval [-π, π].
f(x)=cos(x)
What is 0 Units?
200
The US road sign is typically shaped as a triangle.
What is yield?
200
This is the Infinite Riemann Sum conversion of the definite integral
\int_0^(\pi/2)cos(x)dx
What is
lim_(n\rightarrow\infty)\sum_(k=1)^n(\pi/(2n))cos(\pi/(2n))?
200
This is the definite integral conversion of the Infinite Riemann Sum
lim_(n\rightarrow\infty)\sum_(k=1)^n(9/n)ln(7+(9k)/n)?
What is
\int_7^16 ln(x)dx or \int_0^9ln(7+x)dx?
300
This is the exact area of the function's curve in relation to the x-axis on the closed interval [0, 12].
What is
-15/2+2\pi
Units?
300
This is the approximate area of the function's curve in relation to the x-axis using a Midpoint Riemann Sum with 3 subintervals on the closed interval [1, 10].
What is 91 Units?
300
This degree measurement, in Fahrenheit, is the difference between the freezing point and boiling point of water.
What is 180?
300
This is the Infinite Riemann Sum conversion of the definite integral
\int_3^9(x+2)^2dx
What is
lim_(n\rightarrow\infty)\sum_(k=1)^n(6/n)(5+(6k)/n)^2?
300
This is the definite integral conversion of the Infinite Riemann Sum
lim_(n\rightarrow\infty)\sum_(k=1)^n(\pi/n)4cos((\pik)/n)?
What is
\int_0^\pi 4cos(x)dx?
400
This is the exact area of the function's curve in relation to the x-axis on the closed interval [-4, 8].
What is
10+2\pi
Units?
400
This is the approximate area of the function's curve in relation to the x-axis with appropriate units using a Trapezoidal Sum with 4 subintervals on the closed interval [0, 4].
What is 30.5 milligrams per centimeter?
400
These two wealthy districts in the Hunger Games are known to produce tributes called "Careers" who take joy in participating in said games
What are District 1 and District 2?
400
This is the Infinite Riemann Sum conversion of the definite integral
\int_(\pi/4)^((3\pi)/2)sin(x+(\pi)/3)dx
What is
lim_(n\rightarrow\infty)\sum_(k=1)^n((5\pi)/(4n))sin((7\pi)/12+(5\pi)/(4n))?
400
This is the definite integral conversion of the Infinite Riemann Sum
lim_(n\rightarrow\infty)\sum_(k=1)^n(8/n)9e^(3+(8k)/n)?
What is
\int_3^11 9e^xdx or \int_0^8 9e^(3+x)dx?