195k views
3 votes
Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to four decimal places.

∫¹⁰ √x²+5 dx, n=4
∫₂

M₄ =

1 Answer

3 votes

Final answer:

To approximate the integral ∫¹⁰ √x²+5 dx using the Midpoint Rule with n=4, divide the interval into subintervals, calculate the width and midpoint of each subinterval, evaluate the function at each midpoint, and use the Midpoint Rule formula to approximate the integral.

Step-by-step explanation:

To approximate the integral ∫¹⁰ √x²+5 dx using the Midpoint Rule, divide the interval [1, 10] into 4 subintervals. Calculate the width of each subinterval by subtracting the lower endpoint from the upper endpoint and dividing by n: Δx = (10 - 1) / 4 = 2.25. Find the midpoint of each subinterval by adding the lower endpoint to half of the width: x_i = 1 + (i - 1/2)Δx. Then, evaluate the function at each midpoint value: f(x_i) = √(x_i² + 5). Finally, use the Midpoint Rule formula to approximate the integral: ∫₂M₄ ≈ Δx * (f(x₁) + f(x₂) + f(x₃) + f(x₄)). Round the result to the nearest four decimal places.

User Daronyondem
by
8.5k points

Related questions

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.