Find the integral of xcosx(dx)
Firstly, let's split the equation "xcosx" into two parts to integrate them separately. 1) Let u=x and dv/dx=cosx 2)As the integral of x is 1, du/dx=1 3)To find v, we integrate cosx to get v=sinx Using the formula: The integral of x.dv/dx=uv-integral of v.du/dx So, to reiterate we have: u=x du/dx=1 v=cosx dv/dx=sinx So, using the formula, we need to find uv and the integral of v.du/dx 1) uv=x.sinx=xsinx 2) v.du/dx=sinx.1=sinx By using the formula as listed above: 1) xsinx-integral(sinx)= xsinx-(-cosx)+c= xsinx+cosx+c Therefore, the answer is xsinx+cosx+c
AF
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