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-xsinx
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Integral of -xsinx dx

Limits of integration:

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Piecewise:

The solution

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∫01−xsin⁡(x) dx\int\limits_{0}^{1} - x \sin{\left(x \right)}\, dx 
Integral((-x)*sin(x), (x, 0, 1))
Detail solution

  1. Use integration by parts:

    ∫u⁡dv⁡=u⁡v⁡−∫v⁡du⁡\int \operatorname{u} \operatorname{dv} = \operatorname{u}\operatorname{v} - \int \operatorname{v} \operatorname{du}

    Let u(x)=−xu{\left(x \right)} = - x and let dv⁡(x)=sin⁡(x)\operatorname{dv}{\left(x \right)} = \sin{\left(x \right)}.

    Then du⁡(x)=−1\operatorname{du}{\left(x \right)} = -1.

    To find v(x)v{\left(x \right)}:

    1. The integral of sine is negative cosine:

      ∫sin⁡(x) dx=−cos⁡(x)\int \sin{\left(x \right)}\, dx = - \cos{\left(x \right)}

    Now evaluate the sub-integral.

  2. The integral of cosine is sine:

    ∫cos⁡(x) dx=sin⁡(x)\int \cos{\left(x \right)}\, dx = \sin{\left(x \right)}

  3. Add the constant of integration:

    xcos⁡(x)−sin⁡(x)+constantx \cos{\left(x \right)} - \sin{\left(x \right)}+ \mathrm{constant}

The answer is:

xcos⁡(x)−sin⁡(x)+constantx \cos{\left(x \right)} - \sin{\left(x \right)}+ \mathrm{constant}

The answer (Indefinite) [src] 
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 | -x*sin(x) dx = C - sin(x) + x*cos(x)
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∫−xsin⁡(x) dx=C+xcos⁡(x)−sin⁡(x)\int - x \sin{\left(x \right)}\, dx = C + x \cos{\left(x \right)} - \sin{\left(x \right)}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.901.0-1.0
Plot the graph f(x)
The answer [src] 
-sin(1) + cos(1)
−sin⁡(1)+cos⁡(1)- \sin{\left(1 \right)} + \cos{\left(1 \right)} 
=
= 
-sin(1) + cos(1)
−sin⁡(1)+cos⁡(1)- \sin{\left(1 \right)} + \cos{\left(1 \right)} 
-sin(1) + cos(1)
Numerical answer [src] 
-0.301168678939757
-0.301168678939757
The graph
Integral of -xsinx dx

    Use the examples entering the upper and lower limits of integration.

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