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				   ∫ xex cosx dx= f(x)+c, then find f(x).


6 years ago

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										1)integral by parts take  x and ex cosx as two parts $\int f g\, dx = f \int g\, dx - \int \left ( f' \int g\,dx \right )\, dx.\!$take f=x   and g=ex cosxhere iam giving method for integration for ex cosx ...i think u can solve now right. do practice so that u can get more concept$\int e^{x} \cos (x) \, dx\!$ $u = \cos(x) \Rightarrow du = -\sin(x)\,dx$ $dv = e^x \, dx \Rightarrow v = \int e^x \, dx = e^x$ $\int e^{x} \cos (x) \, dx = e^{x} \cos (x) + \int e^{x} \sin (x) \, dx.\!$ $u = \sin(x) \Rightarrow du = \cos(x)\, dx$ $dv = e^x \, dx \Rightarrow v = \int e^x \, dx = e^x$ $\int e^x \sin (x) \, dx = e^x \sin (x) - \int e^x \cos (x) \,dx$
Putting these together,
$\int e^x \cos (x) \,dx = e^x \cos (x) + e^x \sin (x) - \int e^x \cos (x) \, dx.$ $2 \int e^{x} \cos (x) \, dx = e^{x} ( \sin (x) + \cos (x) ) + C\!$ $\int e^x \cos (x) \,dx = {e^x ( \sin (x) + \cos (x) ) \over 2} + C'\!$Now you can win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian. Now you score 5+15 POINTS by uploading your Pic and Downloading the Askiitians Toolbar : Click here to download the toolbar..

6 years ago

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