Reimann Sum - Midpoint Approximation
- Thread starter Jason76
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This wasn't isn't too hard to figure out
\(\displaystyle \int^{5}_{1} f(x) dx\)
interval: \(\displaystyle [1,5]\)
\(\displaystyle n = 2\) - because it wants two sub-intervals
\(\displaystyle a = 1\)
\(\displaystyle b = 5\)
We use
\(\displaystyle \Delta(x) =\) width \(\displaystyle = \dfrac{b - a}{n} = \dfrac{5 - 1}{2} = 2\)
Now we know that each interval is \(\displaystyle 2\). So now we need to find the midpoint of each interval using the formula: \(\displaystyle M_{1} = \dfrac{L_{1} + R_{2}}{2}\)
We know what \(\displaystyle L_{1}\) and \(\displaystyle R_{2}\) are for each interval, by looking at a graph we will draw.
Now you would have \(\displaystyle (x_{1}), (x_{2})\) which represent each midpoint.
Finally, to find the area under the curve:
\(\displaystyle \Delta(x)[f(x_{1}) + f(x_{2})] = \) area
Look right
\(\displaystyle \int^{5}_{1} f(x) dx\)
interval: \(\displaystyle [1,5]\)
\(\displaystyle n = 2\) - because it wants two sub-intervals
\(\displaystyle a = 1\)
\(\displaystyle b = 5\)
We use
\(\displaystyle \Delta(x) =\) width \(\displaystyle = \dfrac{b - a}{n} = \dfrac{5 - 1}{2} = 2\)
Now we know that each interval is \(\displaystyle 2\). So now we need to find the midpoint of each interval using the formula: \(\displaystyle M_{1} = \dfrac{L_{1} + R_{2}}{2}\)
We know what \(\displaystyle L_{1}\) and \(\displaystyle R_{2}\) are for each interval, by looking at a graph we will draw.
Now you would have \(\displaystyle (x_{1}), (x_{2})\) which represent each midpoint.
Finally, to find the area under the curve:
\(\displaystyle \Delta(x)[f(x_{1}) + f(x_{2})] = \) area
Look right
Last edited:
This wasn't isn't too hard to figure out
\(\displaystyle \int^{5}_{1} f(x) dx\)
interval: \(\displaystyle [1,5]\)
\(\displaystyle n = 2\) - because it wants two sub-intervals
\(\displaystyle a = 1\)
\(\displaystyle b = 5\)
We use
\(\displaystyle \Delta(x) =\) width \(\displaystyle = \dfrac{b - a}{n} = \dfrac{5 - 1}{2} = 2\)
Now we know that each interval is \(\displaystyle 2\). So now we need to find the midpoint of each interval using the formula: \(\displaystyle M_{1} = \dfrac{L_{1} + R_{2}}{2}\)
We know what \(\displaystyle L_{1}\) and \(\displaystyle R_{2}\) are for each interval, by looking at a graph we will draw.
Now you would have \(\displaystyle (x_{1}), (x_{2})\) which represent each midpoint.
Finally, to find the area under the curve:
\(\displaystyle \Delta(x)[f(x_{1}) + f(x_{2})] = \) area
Look right
Looks good. So what did you get for your \(\displaystyle (x_{1}), (x_{2})\)?
The book answer is 32. I will try to figure this one out, step by step, soon.