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Solving integrals/ 1-y^2

Integral of 1-y^2 dx

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

You have entered [src] 
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∫−11(1−y2) dy\int\limits_{-1}^{1} \left(1 - y^{2}\right)\, dy 
Integral(1 - y^2, (y, -1, 1))
Detail solution

  1. Integrate term-by-term:

    1. The integral of a constant is the constant times the variable of integration:

      ∫1 dy=y\int 1\, dy = y

    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}

    The result is: −y33+y- \frac{y^{3}}{3} + y

  2. Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src] 
  /                        
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 | /     2\              y 
 | \1 - y / dy = C + y - --
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∫(1−y2) dy=C−y33+y\int \left(1 - y^{2}\right)\, dy = C - \frac{y^{3}}{3} + y
Simplify
The graph
-1.0-0.8-0.6-0.4-0.21.00.00.20.40.60.82-2
Plot the graph f(x)
The answer [src] 
4/3
43\frac{4}{3} 
=
= 
4/3
43\frac{4}{3} 
4/3
Numerical answer [src] 
1.33333333333333
1.33333333333333

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

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