Question

Attached as photo. Please help

Answer 1

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:

1. Define the function seen in the statement by the label f(x₀, y₀).
2. Determine the different variables by the following formulas:
   
   xₙ₊₁ = xₙ + (n + 1) · Δx     (2)
   yₙ₊₁ = yₙ + Δx · f(xₙ, yₙ)     (3)
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: brainly.com/question/16807646

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