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Integral of -y dy

Limits of integration:

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v

The graph:

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Piecewise:

The solution

You have entered [src] 
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0
∫01(−y) dy\int\limits_{0}^{1} \left(- y\right)\, dy 
Integral(-y, (y, 0, 1))
Detail solution

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

    ∫(−y) dy=−∫y dy\int \left(- y\right)\, dy = - \int y\, dy

    1. The integral of yny^{n} is yn+1n+1\frac{y^{n + 1}}{n + 1} when n≠−1n \neq -1:

      ∫y dy=y22\int y\, dy = \frac{y^{2}}{2}

    So, the result is: −y22- \frac{y^{2}}{2}

  2. Add the constant of integration:

    −y22+constant- \frac{y^{2}}{2}+ \mathrm{constant}

The answer is:

−y22+constant- \frac{y^{2}}{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /             2
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 | -y dy = C - --
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∫(−y) dy=C−y22\int \left(- y\right)\, dy = C - \frac{y^{2}}{2}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.901-2
Plot the graph f(x)
The answer [src] 
-1/2
−12- \frac{1}{2} 
=
= 
-1/2
−12- \frac{1}{2} 
-1/2
Numerical answer [src] 
-0.5
-0.5
The graph
Integral of -y dy

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

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