Using the Trapezoidal rule, find the approxim | vedclass

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(C) The Trapezoidal rule for $n$ intervals is given by:$\int_{x_0}^{x_n} y \, dx \approx \frac{h}{2} [y_0 + 2(y_1 + y_2 + \dots + y_{n-1}) + y_n]$Here

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$2$

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(C) The Trapezoidal rule for $n$ intervals is given by:$\int_{x_0}^{x_n} y \, dx \approx \frac{h}{2} [y_0 + 2(y_1 + y_2 + \dots + y_{n-1}) + y_n]$Here, the values are $x_0=1, x_1=2, x_2=3, x_3=4$, so the step size $h = x_1 - x_0 = 2 - 1 = 1$.The corresponding $y$ values are $y_0 = 0.7111, y_1 = 0.7222, y_2 = 0.7333, y_3 = 0.7444$.Substituting these into the formula:$\int_1^4 y \, dx \approx \frac{1}{2} [0.7111 + 2(0.7222 + 0.7333) + 0.7444]$$\int_1^4 y \, dx \approx \frac{1}{2} [0.7111 + 2(1.4555) + 0.7444]$$\int_1^4 y \, dx \approx \frac{1}{2} [0.7111 + 2.9110 + 0.7444]$$\int_1^4 y \, dx \approx \frac{1}{2} [4.3665]$$\int_1^4 y \, dx \approx 2.18325 \approx 2.1833$Thus, the correct option is $C$.

$x$	$1$	$2$	$3$	$4$
$y$	$0.7111$	$0.7222$	$0.7333$	$0.7444$

Using the Trapezoidal rule, find the approximate value of $\int_1^4 y \, dx$ based on the following data:
$x$ $1$ $2$ $3$ $4$
$y$ $0.7111$ $0.7222$ $0.7333$ $0.7444$
(in $.1833$)

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Using the Trapezoidal rule, find the approximate value of $\int_1^4 y \, dx$ based on the following data:$x$$1$$2$$3$$4$$y$$0.7111$$0.7222$$0.7333$$0.7444$ (in $.1833$)