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-y^2

Integral of -y^2 dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src]
  1       
  /       
 |        
 |    2   
 |  -y  dy
 |        
/         
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=y2dy\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 n1n \neq -1:

      y2dy=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 
/                 
(y2)dy=Cy33\int \left(- y^{2}\right)\, dy = C - \frac{y^{3}}{3}
The graph
0.001.000.100.200.300.400.500.600.700.800.901-2
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.