Lösung 2.1:3b
Aus Online Mathematik Brückenkurs 2
(Unterschied zwischen Versionen)
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As the integral stands, it is not so easy to see what the primitive functions are, but if we use the formula for double angles, | As the integral stands, it is not so easy to see what the primitive functions are, but if we use the formula for double angles, | ||
| - | {{ | + | {{Abgesetzte Formel||<math>\int 2\sin x\cos x\,dx = \int \sin 2x\,dx</math>}} |
we obtain a standard integral where we can write down the primitive functions directly, | we obtain a standard integral where we can write down the primitive functions directly, | ||
| - | {{ | + | {{Abgesetzte Formel||<math>\int \sin 2x\,dx = -\frac{\cos 2x}{2}+C\,,</math>}} |
where <math>C</math> is an arbitrary constant. | where <math>C</math> is an arbitrary constant. | ||
Version vom 12:58, 10. Mär. 2009
As the integral stands, it is not so easy to see what the primitive functions are, but if we use the formula for double angles,
| \displaystyle \int 2\sin x\cos x\,dx = \int \sin 2x\,dx |
we obtain a standard integral where we can write down the primitive functions directly,
| \displaystyle \int \sin 2x\,dx = -\frac{\cos 2x}{2}+C\,, |
where \displaystyle C is an arbitrary constant.
