Solution 2.1:3a

From Förberedande kurs i matematik 2

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Current revision (13:11, 21 October 2008) (edit) (undo)
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The notation ''<math>\int{\sin x\,dx}</math>'' is called the indefinite integral of
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The notation "<math>\smallint\sin x\,dx</math>" is called the indefinite integral of
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<math>\sin x</math>
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<math>\sin x</math> and means all primitive functions of <math>\sin x</math>.
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and means all primitive functions of
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<math>\sin x</math>.
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Because
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Because <math>\sin x</math> is a standard function, we know from the course notes that its primitive functions are
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<math>\sin x</math>
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is a standard function, we know from the course notes that its primitive functions are
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{{Displayed math||<math>\int{\sin x\,dx}=-\cos x+C\,,</math>}}
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<math>\int{\sin x\,dx}=-\cos x+C</math>
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where <math>C</math> is an arbitrary constant.
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where
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<math>C</math>
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is an arbitrary constant.
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Current revision

The notation "\displaystyle \smallint\sin x\,dx" is called the indefinite integral of \displaystyle \sin x and means all primitive functions of \displaystyle \sin x.

Because \displaystyle \sin x is a standard function, we know from the course notes that its primitive functions are

\displaystyle \int{\sin x\,dx}=-\cos x+C\,,

where \displaystyle C is an arbitrary constant.

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