riemann 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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(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

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∫₀⁸sin(√x)dx, n=4

Solution

6.18203…

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Solve by:

Solve by midpoint Riemann sum

Solve by left point Riemann sum

Solve by right point Riemann sum

Solve by trapezoidal rule

Solve by Simpson's rule

One step at a time

Riemann sum using midpoint of subinterval

∫_a^bf(x)dx ≈ Δ x(f(x₀+x₁2 )+f(x₁+x₂2 )+f(x₂+x₃2 )+...+f(x_n−1+x_n2 )),
where Δ x = b−an

Apply Riemann Formula

=2(f(x₀+x₁2 )+f(x₁+x₂2 )+f(x₂+x₃2 )+f(x₃+x₄2 ))

Calculate Sub Intervals

=2(sin(1)+sin(√3)+sin(√5)+sin(√7))

=6.18203…

Midpoint Rule Examples

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

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

Solution

Solution steps

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