Question

Use the Trapezoidal Rule with n = 4 steps to estimate the integral.\\ $\int_0^2 (x^4+1) dx$\\ You may use one of the following formulas:\\ $M(n) = f(m_1)\Delta x + f(m_2)\Delta x + ... + f(m_n)\Delta x = \sum_{k=1}^n f(\frac{x_{k-1}+x_k}{2})\Delta x$\\ $T(n) = [\frac{1}{2}f(x_0) + \sum_{i=1}^{n-1} f(x_i) + \frac{1}{2}f(x_n)]\Delta x$\\ A. $\frac{145}{16}$\ B. $\frac{101}{12}$\ C. $\frac{145}{8}$\ D. $\frac{217}{16}$

          Use the Trapezoidal Rule with n = 4 steps to estimate the integral.\\
$\int_0^2 (x^4+1) dx$\\
You may use one of the following formulas:\\
$M(n) = f(m_1)\Delta x + f(m_2)\Delta x + ... + f(m_n)\Delta x = \sum_{k=1}^n f(\frac{x_{k-1}+x_k}{2})\Delta x$\\
$T(n) = [\frac{1}{2}f(x_0) + \sum_{i=1}^{n-1} f(x_i) + \frac{1}{2}f(x_n)]\Delta x$\\
A. $\frac{145}{16}$\
B. $\frac{101}{12}$\
C. $\frac{145}{8}$\
D. $\frac{217}{16}$

Use the Trapezoidal Rule with n = 4 steps to estimate the integral.

∫0^2 (x^4+1) dx

You may use one of the following formulas:

M(n) = f(m1)Δ x + f(m2)Δ x + ... + f(mn)Δ x = ∑k=1^n f((xk-1+xk)/(2))Δ x

T(n) = [(1)/(2)f(x0) + ∑i=1^n-1 f(xi) + (1)/(2)f(xn)]Δ x

A. (145)/(16)B. (101)/(12)C. (145)/(8)D. (217)/(16)

Added by Michael H.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Alec Traaseth

Step 1

Δx = (b - a) / n = (2 - 0) / 4 = 0.5 x0 = 0 x1 = 0.5 x2 = 1 x3 = 1.5 x4 = 2 Show more…

Show all steps

Thanks for your feedback!

Use the Trapezoidal Rule with n = 4 steps to estimate the integral of âˆ«(x^4+1)dx from 0 to 2. You may use one of the following formulas: M(n) = (Î”x/2) * (f(x0) + 2f(x1) + 2f(x2) + ... + 2f(xn-1) + f(xn))