integral from 0 to pi of sinxcos^2x

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

☐²

x^☐

√☐

^□√☐

□□

log_□

θ

∞

∫

ddx

≥	≤	·	÷	`x`^◦	(☐)	\|☐\|	(`f` ◦ `g`)	`f`(`x`)	ln	`e`^☐
(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

simplify solve for inverse tangent line

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∫₀^πsin(x)cos²(x)dx

Solution

Decimal

0.66666…

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Solution steps

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∫₀^πsin(x)cos²(x)dx

Apply u-substitution: ∫₁⁻¹−u²du

=∫₁⁻¹−u²du

∫_a^bf(x)dx=−∫_b^af(x)dx, a<b

=−∫₋₁¹−u²du

Take the constant out: ∫a·f(x)dx=a·∫f(x)dx

=−(−∫₋₁¹u²du)

Apply the Power Rule: [u³3 ]₋₁¹

=−(−[u³3 ]₋₁¹)

Simplify

=[u³3 ]₋₁¹

Compute the boundaries: 23

=23

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

integral from 0 to pi of sinxcos^2x

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