Question
Studdy Solution
STEP 1
What is this asking?
We need to find the definite integral of from 0 to 16 using the Simpson's rule with four intervals.
Watch out!
Remember that Simpson's rule requires an **even** number of intervals, and we have that here!
Also, don't forget to calculate the width of each interval correctly.
STEP 2
1. Calculate the width of each interval.
2. Apply Simpson's rule.
STEP 3
Alright, let's **start** by finding the width of each interval, which we'll call *h*.
We take the **difference** between the **upper** and **lower limits** of integration (16 and 0, respectively), and then **divide** by the **number of intervals**, which is **4**.
STEP 4
So, we have .
Our interval width is **4**!
STEP 5
Now, let's use Simpson's rule!
Remember, it looks like this:
where *h* is the **width** of each interval, and are the points at the start of each interval.
STEP 6
In our case, , , and .
Let's list out our values: , , , , and .
STEP 7
Now, we need to **evaluate** our function, , at each of these values:
STEP 8
Let's **plug** everything into Simpson's rule:
STEP 9
Using Simpson's rule with four intervals, the approximate value of the definite integral is **10.4389**.
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