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Solving integrals/ 2-y^2

Integral of 2-y^2 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  2            
  /            
 |             
 |  /     2\   
 |  \2 - y / dy
 |             
/              
-1
$$\int\limits_{-1}^{2} \left(2 - y^{2}\right)\, dy$$ 
Integral(2 - y^2, (y, -1, 2))
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. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                          
 |                          3
 | /     2\                y 
 | \2 - y / dy = C + 2*y - --
 |                         3 
/
$$\int \left(2 - y^{2}\right)\, dy = C - \frac{y^{3}}{3} + 2 y$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
3
$$3$$ 
=
= 
3
$$3$$ 
3
Numerical answer [src] 
3.0
3.0

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

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