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sin(0)

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`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

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≥	≤	·	÷	`x`^◦	(☐)	\|☐\|	(`f` ◦ `g`)	`f`(`x`)	ln	`e`^☐
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Steps Examples

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∫₀⁵sin(x²)dx, n=5

Solution

0.14270…

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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

=12 (f(x₀)+2f(x₁)+2f(x₂)+2f(x₃)+2f(x₄)+f(x₅))

Calculate Sub Intervals

=12 (0+2sin(1)+2sin(4)+2sin(9)+2sin(16)+sin(25))

=0.14270…

Multiply Complex Numbers Examples

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أهلاً, اطرح سؤالا حول ∫₀⁵sin(x²)dx,n=5 أو اختر من الخيارات أدناه

حل بواسطة: midpoint Riemann sum

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Notebook

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

sin(0)

Solution

Solution steps

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