By Euler's method the <em>numerical approximate</em> solution of the <em>definite</em> integral is 4.189 648.
<h3>How to estimate a definite integral by numerical methods</h3>
In this problem we must make use of Euler's method to estimate the upper bound of a <em>definite</em> integral. Euler's method is a <em>multi-step</em> method, related to Runge-Kutta methods, used to estimate <em>integral</em> values numerically. By integral theorems of calculus we know that definite integrals are defined as follows:
∫ f(x) dx = F(b) - F(a) (1)
The steps of Euler's method are summarized below:
- Define the function seen in the statement by the label f(x₀, y₀).
- Determine the different variables by the following formulas:
xₙ₊₁ = xₙ + (n + 1) · Δx (2)
yₙ₊₁ = yₙ + Δx · f(xₙ, yₙ) (3) - Find the integral.
The table for x, f(xₙ, yₙ) and y is shown in the image attached below. By direct subtraction we find that the <em>numerical</em> approximation of the <em>definite</em> integral is:
y(4) ≈ 4.189 648 - 0
y(4) ≈ 4.189 648
By Euler's method the <em>numerical approximate</em> solution of the <em>definite</em> integral is 4.189 648.
To learn more on Euler's method: brainly.com/question/16807646
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Answer:
K 2
J 4
Step-by-step explanation:
Solved it as an equation 2 x+x=6
x= number of miles Katie drives
Answer:
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Painting Media
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Step-by-step explanation:
Answer:
An employee would have to work 20 years in order to receive an annual pay of $45,000
A= π r2 and v=3.14d
---Volume(v=3.14d):
3.14(15) equals 47.1
47.1 rounds to 47
nearest hundreth would be 0 that rounds to .1 or .10,which rounds to 47
v=47
---Area(π r2)
3.14(7.5)^2 is 3.14(56.25)
176.625
176.625 rounded to the nearest hundreth is 176.630.
Answer:
The area of a circle with the diameter of 15 is 176.630.
