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trapezoidal integral from 0 to 8 of sin(sqrt(x)), n=4

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(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

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∫₀⁸sin(√x)dx, n=4

Solution

5.37851…

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Solve by:

Solve by trapezoidal rule

Solve by midpoint Riemann sum

Solve by left point Riemann sum

Solve by right point Riemann sum

Solve by Simpson's rule

One step at a time

Trapezoidal Rule (Approximation)

Average of Left and Right Endpoint approximations:
∫_a^bf(x)dx ≈ Δ x2 (f(x₀)+2f(x₁)+...+2f(x_n−1)+f(x_n))
where Δ x = b−an

Apply Trapezoidal Formula

=1· (f(x₀)+2f(x₁)+2f(x₂)+2f(x₃)+f(x₄))

Calculate Sub Intervals

=1· (0+2sin(√2)+2sin(2)+2sin(√6)+sin(2√2))

=5.37851…

Trapezoidal Approximation Examples

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Solve by: midpoint Riemann sum

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Solve by: right point Riemann sum

Solve by: Simpson's rule

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−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
▭ \|▭	)	.	0	=	+	`y`

trapezoidal integral from 0 to 8 of sin(sqrt(x)), n=4

Solution

Solution steps

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