How do you integrate #sin^(3)2xdx#?
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There's no obvious replacement and no obvious parts, so I can't integrate right away.
That covers if in calculus. In trigonometry, there are additional
Try it:
I ought to be able to combine each of these two terms now:
Thus, we obtain:
Or view the alternative solution I'll share.
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To integrate sin^(3)(2x) dx, you can use the trigonometric identity:
sin^3(2x) = (1/4)(3sin(2x) - sin(6x))
Then, integrate each term separately:
∫(1/4)(3sin(2x) - sin(6x)) dx
= (1/4) * (∫3sin(2x) dx - ∫sin(6x) dx)
= (1/4) * (-3/2cos(2x) + (1/6)cos(6x)) + C
= -(3/8)cos(2x) + (1/24)cos(6x) + C
where C is the constant of integration.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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