Use Simpson's Rule with to approximate . Round to 3 decimal places.

Question

Use Simpson's Rule with  to approximate  . Round to 3 decimal places.

Quizplus · Accepted Answer

Using Simpson's Rule with 11eaa948_cd2c_18d4_84bc_e3398d0cc340_TB2342_11, we have:

h = (1-0)/10 = 0.1

x0 = 0, x1 = 0.1, x2 = 0.2, …, x10 = 1

f(x0) = 11eaa948_cd2c_18d4_84bc_e3398d0cc340_TB2342_11 = 1

f(x1) = 11eaa948_cd2c_18d4_84bc_e3398d0cc340_TB2342_11 = 1.1

f(x2) = 11eaa948_cd2c_18d4_84bc_e3398d0cc340_TB2342_11 = 1.2

and so on.

Using the formula for Simpson's Rule, we have:

11eaa948_cd2c_18d5_84bc_c112b6eb0245_TB2342_11 ≈ h/3[f(x0) + 4f(x1) + 2f(x2) + 4f(x3) + 2f(x4) + 4f(x5) + 2f(x6) + 4f(x7) + 2f(x8) + 4f(x9) + f(x10)]

= 0.1/3[1 + 4(1.1) + 2(1.2) + 4(1.3) + 2(1.4) + 4(1.5) + 2(1.6) + 4(1.7) + 2(1.8) + 4(1.9) + 2]

= 0.1/3[38.28]

= 0.01276

Rounding to 3 decimal places, we get:

11eaa948_cd2c_18d5_84bc_c112b6eb0245_TB2342_11 ≈ 0.013

So the best choice is B: 11eaa948_cd2c_3fe7_84bc_cb15870449a1_TB2342_11.

Use Simpson's Rule with to Approximate