Riemann Sums. Width of partition:. Adds the rectangles, where n is the number of partitions (rectangles). Height of rectangle for each of the x-values in the interval. What is a Riemann Sum?. Takes approximating the area under a curve with rectangles to the next level LOOKS LIKE:.
Width of partition:
Adds the rectangles, where n is the number of partitions (rectangles)
Height of rectangle for each of the x-values in the interval
If the number of partitions is allowed to approach infinity…what happens?
That’s right! The rectangular approximation approaches the EXACT area under the curve! How do we do it?
READ LIKE THIS:
The integral, from a to b, of f(x) with respect to x
Integrand (between the integral sign and the dx)
Upper (right) limit of integration
Integral sign (originated from the summation sign, Sigma)
Lower (left) limit of integration
Tells you the variable of integration (who is the variable)
Where x is between 0 and 2.
Where x is between 3 and 7.
Where x is between -2 and 2.
Why is it called a definite integral?
Because the integral sign includes limits of integration!
Why is this okay?