Use Simpson's Rule to approximate the value of the definite integral with . Round your answer to four decimal places.

Question

Use Simpson's Rule to approximate the value of the definite integral  with  . Round your answer to four decimal places.

Quizplus · Accepted Answer

Using Simpson's Rule, we have:

∫(0 to 2) e^(x^2) dx

= [f(0) + 4f(1) + f(2)](2/6)

where f(x) = e^(x^2).

Thus, we need to evaluate f(0), f(1), and f(2):

f(0) = e^(0^2) = 1
f(1) = e^(1^2) ≈ 2.7183
f(2) = e^(2^2) ≈ 54.5982

Plugging these values into the formula, we get:

∫(0 to 2) e^(x^2) dx ≈ [1 + 4(2.7183) + 54.5982](2/6) ≈ 5.5358

Rounded to four decimal places, this is approximately 5.5358, which corresponds to choice C.

Use Simpson's Rule to Approximate the Value of the Definite