Use Simpson's Rule with n = 4 to estimate the length of the arc of the curve with equations , from to . Round your answer to four decimal places.
E)None of these

Question

Use Simpson's Rule with n = 4 to estimate the length of the arc of the curve with equations  , from  to  . Round your answer to four decimal places.
E)None of these

Quizplus · Accepted Answer

Using Simpson's Rule with n = 4, we have:

h = (b-a)/n = (11eaa3e5_54f6_7eab_9f8f_bd74ba3efe14_TB5971_11 - 11eaa3e5_54f6_579a_9f8f_1d8b4eade0c0_TB5971_11)/4 = 0.125

x0 = 11eaa3e5_54f6_579a_9f8f_1d8b4eade0c0_TB5971_11, x1 = 11eaa3e5_54f6_579c_9f8f_8af88fd1e047_TB5971_11, x2 = 11eaa3e5_54f6_7eab_9f8f_1fe4220e5e5d_TB5971_11, x3 = 11eaa3e5_54f6_7ead_9f8f_efd0b7ca8ae2_TB5971_11, x4 = 11eaa3e5_54f6_7eaf_9f8f_4a4e4adec768_TB5971_11

f(x0) = f(11eaa3e5_54f6_579a_9f8f_1d8b4eade0c0_TB5971_11) = 2(11eaa3e5_54f6_579a_9f8f_1d8b4eade0c0_TB5971_11) + 3 = 23
f(x1) = f(11eaa3e5_54f6_579c_9f8f_8af88fd1e047_TB5971_11) = 2(11eaa3e5_54f6_579c_9f8f_8af88fd1e047_TB5971_11) + 3 = 23.25
f(x2) = f(11eaa3e5_54f6_7eab_9f8f_1fe4220e5e5d_TB5971_11) = 2(11eaa3e5_54f6_7eab_9f8f_1fe4220e5e5d_TB5971_11) + 3 = 24.5
f(x3) = f(11eaa3e5_54f6_7ead_9f8f_efd0b7ca8ae2_TB5971_11) = 2(11eaa3e5_54f6_7ead_9f8f_efd0b7ca8ae2_TB5971_11) + 3 = 23.75
f(x4) = f(11eaa3e5_54f6_7eaf_9f8f_4a4e4adec768_TB5971_11) = 2(11eaa3e5_54f6_7eaf_9f8f_4a4e4adec768_TB5971_11) + 3 = 22

Now, we can use Simpson's Rule formula:

∫_a^b f(x) dx ≈ h/3 [f(x0) + 4f(x1) + 2f(x2) + 4f(x3) + f(x4)]
≈ 0.125/3 [23 + 4(23.25) + 2(24.5) + 4(23.75) + 22]
≈ 7.9749

Rounding to four decimal places, we get 7.9749 ≈ 7.9748, which matches answer C: 11eaa3e5_54f6_7eae_9f8f_d7b4ba4229aa_TB5971_11

Use Simpson's Rule with N = 4 to Estimate the Length