The values of a function f(x) at different va | vedclass

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(C) The Trapezoidal rule for approximating the integral $\int_{x_0}^{x_n} f(x) dx$ is given by:$\int_{x_0}^{x_n} f(x) dx \approx \frac{h}{2} [ (y_0 +

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$52.5$

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(C) The Trapezoidal rule for approximating the integral $\int_{x_0}^{x_n} f(x) dx$ is given by:$\int_{x_0}^{x_n} f(x) dx \approx \frac{h}{2} [ (y_0 + y_n) + 2(y_1 + y_2 + \dots + y_{n-1}) ]$Here,$h = 1$ (the difference between consecutive $x$ values).The values are $y_0=2, y_1=3, y_2=6, y_3=11, y_4=18, y_5=27$.Substituting these values into the formula:Area $\approx \frac{1}{2} [ (2 + 27) + 2(3 + 6 + 11 + 18) ]$Area $\approx \frac{1}{2} [ 29 + 2(38) ]$Area $\approx \frac{1}{2} [ 29 + 76 ]$Area $\approx \frac{1}{2} [ 105 ] = 52.5$ square units.

$x$	$0$	$1$	$2$	$3$	$4$	$5$
$f(x)$	$2$	$3$	$6$	$11$	$18$	$27$

The values of a function $f(x)$ at different values of $x$ are given in the table below:
$x$ $0$ $1$ $2$ $3$ $4$ $5$
$f(x)$ $2$ $3$ $6$ $11$ $18$ $27$

Then,the approximate area (in square units) bounded by the curve $y=f(x)$ and the $x$-axis between $x=0$ and $x=5$,using the Trapezoidal rule,is

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The values of a function $f(x)$ at different values of $x$ are given in the table below:$x$$0$$1$$2$$3$$4$$5$$f(x)$$2$$3$$6$$11$$18$$27$Then,the approximate area (in square units) bounded by the curve $y=f(x)$ and the $x$-axis between $x=0$ and $x=5$,using the Trapezoidal rule,is