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-y^2
Solving integrals/ -y^2

Integral of -y^2 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1       
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 |    2   
 |  -y  dy
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0
∫01(−y2) dy\int\limits_{0}^{1} \left(- y^{2}\right)\, dy 
Integral(-y^2, (y, 0, 1))
Detail solution

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

    ∫(−y2) dy=−∫y2 dy\int \left(- y^{2}\right)\, dy = - \int y^{2}\, dy

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

      ∫y2 dy=y33\int y^{2}\, dy = \frac{y^{3}}{3}

    So, the result is: −y33- \frac{y^{3}}{3}

  2. Add the constant of integration:

    −y33+constant- \frac{y^{3}}{3}+ \mathrm{constant}

The answer is:

−y33+constant- \frac{y^{3}}{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /               
 |               3
 |   2          y 
 | -y  dy = C - --
 |              3 
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∫(−y2) dy=C−y33\int \left(- y^{2}\right)\, dy = C - \frac{y^{3}}{3}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.901-2
Plot the graph f(x)
The answer [src] 
-1/3
−13- \frac{1}{3} 
=
= 
-1/3
−13- \frac{1}{3} 
-1/3
Numerical answer [src] 
-0.333333333333333
-0.333333333333333
The graph
Integral of -y^2 dx

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

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