How do you find the integral of # Cos(2x)Sin(x)dx#?
Multiply out.
The sines under the integral cancel each other out.
Separate the integrals.
Finally, combine like terms.
Hopefully this helps!
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To find the integral of ( \cos(2x)\sin(x) ), you can use integration by parts method. Let ( u = \sin(x) ) and ( dv = \cos(2x)dx ). Then, ( du = \cos(x)dx ) and ( v = \frac{1}{2}\sin(2x) ).
Applying the integration by parts formula:
[ \int u dv = uv - \int v du ]
Substituting the values:
[ \int \cos(2x)\sin(x)dx = \frac{1}{2}\sin(2x)\sin(x) - \int \frac{1}{2}\sin(2x)\cos(x)dx ]
Now, you can integrate the remaining integral using the same method, or through trigonometric identities.
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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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