Complete the following exercises on the outcomes below. Explain anything that is not clear or obvious as you are showing how well you understand a topic.
Outcome I2: Using Riemann Sums to Find Areas
Use the limit process to find the area between
y=4-x^(2)
, the
x
-axis, and the vertical lines
x=0
and
x=3
.
a) Find the width of the rectangles:
,\Delta x=
b) Find the endpoints of the rectangles:
x_(i)=
c) Find the function at the endpoints:
f(x_(i))=
d) Using the summation notation find:
S_(n)=\sum_(i=1)^n f(x_(i))\Delta x
e) Find the value for the total area by letting the number of rectangles
n->\infty
:
\lim_(n->\infty )S_(n)