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Solving integrals/ xcos(pi)xdx

Integral of xcos(pi)xdx d0

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
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 |  x*cos(pi)*x dx
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∫012xxcos⁡(π) dx\int\limits_{0}^{\frac{1}{2}} x x \cos{\left(\pi \right)}\, dx 
Integral((x*cos(pi))*x, (x, 0, 1/2))
Detail solution

  1. Rewrite the integrand:

    xxcos⁡(π)=−x2x x \cos{\left(\pi \right)} = - x^{2}

  2. The integral of a constant times a function is the constant times the integral of the function:

    ∫(−x2) dx=−∫x2 dx\int \left(- x^{2}\right)\, dx = - \int x^{2}\, dx

    1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n≠−1n \neq -1:

      ∫x2 dx=x33\int x^{2}\, dx = \frac{x^{3}}{3}

    So, the result is: −x33- \frac{x^{3}}{3}

  3. Add the constant of integration:

    −x33+constant- \frac{x^{3}}{3}+ \mathrm{constant}

The answer is:

−x33+constant- \frac{x^{3}}{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                      3
 |                      x 
 | x*cos(pi)*x dx = C - --
 |                      3 
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∫xxcos⁡(π) dx=C−x33\int x x \cos{\left(\pi \right)}\, dx = C - \frac{x^{3}}{3}
Simplify
The graph
0.000.500.050.100.150.200.250.300.350.400.45-0.500.25
Plot the graph f(x)
The answer [src] 
-1/24
−124- \frac{1}{24} 
=
= 
-1/24
−124- \frac{1}{24} 
-1/24
Numerical answer [src] 
-0.0416666666666667
-0.0416666666666667

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

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