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Solving integrals/ 1-y^2

Integral of 1-y^2 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1            
  /            
 |             
 |  /     2\   
 |  \1 - y / dy
 |             
/              
-1
$$\int\limits_{-1}^{1} \left(1 - y^{2}\right)\, dy$$ 
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. The integral of a constant times a function is the constant times the integral of the function:

      1. The integral of is when :

      So, the result is:

    The result is:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                        
 |                        3
 | /     2\              y 
 | \1 - y / dy = C + y - --
 |                       3 
/
$$\int \left(1 - y^{2}\right)\, dy = C - \frac{y^{3}}{3} + y$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
4/3
$$\frac{4}{3}$$ 
=
= 
4/3
$$\frac{4}{3}$$ 
4/3
Numerical answer [src] 
1.33333333333333
1.33333333333333

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

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