integral of sin^2(θ)

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

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log_□

θ

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ddx

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

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Steps Examples

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∫ sin²(θ)dθ

Solution

12 (θ−12 sin(2θ))+C

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Solution steps

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∫ sin²(θ)dθ

Rewrite using trig identities

=∫ 1−cos(2θ)2 dθ

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

=12 · ∫ 1−cos(2θ)dθ

Apply the Sum Rule: ∫f(x)±g(x)dx=∫f(x)dx±∫g(x)dx

=12 (∫ 1dθ−∫ cos(2θ)dθ)

∫ 1dθ=θ

∫ cos(2θ)dθ=12 sin(2θ)

=12 (θ−12 sin(2θ))

Add a constant to the solution

=12 (θ−12 sin(2θ))+C

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