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Solving integrals/ 1/2y+y^2

Integral of 1/2y+y^2 dy

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1            
  /            
 |             
 |  /y    2\   
 |  |- + y | dy
 |  \2     /   
 |             
/              
0
$$\int\limits_{0}^{1} \left(y^{2} + \frac{y}{2}\right)\, dy$$ 
Integral(y/2 + y^2, (y, 0, 1))
Detail solution

  1. Integrate term-by-term:

    1. The integral of is when :

    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    y 
 | |- + y | dy = C + -- + --
 | \2     /          3    4 
 |                          
/
$$\int \left(y^{2} + \frac{y}{2}\right)\, dy = C + \frac{y^{3}}{3} + \frac{y^{2}}{4}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
7/12
$$\frac{7}{12}$$ 
=
= 
7/12
$$\frac{7}{12}$$ 
7/12
Numerical answer [src] 
0.583333333333333
0.583333333333333

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

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