By Euler's method the numerical approximate solution of the definite integral is 4.189 648.
How to estimate a definite integral by numerical methods
In this problem we must make use of Euler's method to estimate the upper bound of a definite integral. Euler's method is a multi-step method, related to Runge-Kutta methods, used to estimate integral 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 numerical approximation of the definite integral is:
y(4) ≈ 4.189 648 - 0
y(4) ≈ 4.189 648
By Euler's method the numerical approximate solution of the definite integral is 4.189 648.
To learn more on Euler's method: https://brainly.com/question/16807646
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