range of cos(2t)

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

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

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∫ sin(2x)dx

Solution

−12 cos(2x)+C

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Solution steps

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∫ sin(2x)dx

Apply u-substitution: ∫ sin(u)12 du

=∫ sin(u)12 du

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

=12 · ∫ sin(u)du

Use the common integral: ∫ sin(u)du=−cos(u)

=12 (−cos(u))

Substitute back u=2x

=12 (−cos(2x))

Simplify

=−12 cos(2x)

Add a constant to the solution

=−12 cos(2x)+C

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range of cos(2t)

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