6.4 Q5.) Use Simpson's rule to approximate
1 answer:
For f(x) = 12/(1+x²), and subinterval width 4, you are to evaluate f(1), f(5), and f(9) and combine them according to the rule
... Integral ≈ (4/3)(f(1) + 4·f(5) + f(9)) = (4/3)(6.0000 + 4·0.4615 + 0.1463) ≈ 10.66
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Simpson's rule has you combine values of f(x) with coefficients 1, 4, 2, 4, ..., 2, 4, 1, where those values are evenly spaced at the edges of an even number of subintervals. Since we have only 3 values to combine, there are no terms that have a coefficient of 2. The entire sum is multiplied by 1/3 the subinterval width.
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Answer:
Step-by-step explanation:
Hi there!
Because we're given the vertex of the parabola, we can determine its equation in vertex form:
where the vertex is
Plug in the vertex (0,0)
Now, we must solve for a. Plug in the given point (-2,3) and solve for a:
Therefore, the value of a is . Plug this back into
:
I hope this helps!