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Solving integrals/ 1+y^2

Integral of 1+y^2 dy

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

Detail solution

  1. Integrate term-by-term:

    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}

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

      ∫1 dy=y\int 1\, dy = y

    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] 
  /                        
 |                        3
 | /     2\              y 
 | \1 + y / dy = C + y + --
 |                       3 
/
∫(y2+1) dy=C+y33+y\int \left(y^{2} + 1\right)\, dy = C + \frac{y^{3}}{3} + y
Simplify
The graph
1.03.01.21.41.61.82.02.22.42.62.8020
Plot the graph f(x)
The answer [src] 
32/3
323\frac{32}{3} 
=
= 
32/3
323\frac{32}{3} 
32/3
Numerical answer [src] 
10.6666666666667
10.6666666666667

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

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