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Identical expressions
sqrt(two)*y^ two
square root of (2) multiply by y squared
square root of (two) multiply by y to the power of two
√(2)*y^2
sqrt(2)*y2
sqrt2*y2
sqrt(2)*y²
sqrt(2)*y to the power of 2
sqrt(2)y^2
sqrt(2)y2
sqrt2y2
sqrt2y^2

Integral of sqrt(2)*y^2 dy

The solution

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  1            
  /            
 |             
 |    ___  2   
 |  \/ 2 *y  dy
 |             
/              
0

$$\int\limits_{0}^{1} \sqrt{2} y^{2}\, dy$$

Integral(sqrt(2)*y^2, (y, 0, 1))

Detail solution

The integral of a constant times a function is the constant times the integral of the function:

$\int \sqrt{2} y^{2}\, dy = \sqrt{2} \int y^{2}\, dy$
1. The integral of $y^{n}$ is $\frac{y^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int y^{2}\, dy = \frac{y^{3}}{3}$
So, the result is: $\frac{\sqrt{2} y^{3}}{3}$
Add the constant of integration:

$\frac{\sqrt{2} y^{3}}{3}+ \mathrm{constant}$

The answer is:

$\frac{\sqrt{2} y^{3}}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                          
 |                     ___  3
 |   ___  2          \/ 2 *y 
 | \/ 2 *y  dy = C + --------
 |                      3    
/

$$\int \sqrt{2} y^{2}\, dy = C + \frac{\sqrt{2} y^{3}}{3}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

  ___
\/ 2 
-----
  3

$$\frac{\sqrt{2}}{3}$$

  ___
\/ 2 
-----
  3

$$\frac{\sqrt{2}}{3}$$

sqrt(2)/3

Numerical answer [src]

0.471404520791032

0.471404520791032

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

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Identical expressions

Integral of sqrt(2)*y^2 dy

Limits of integration:

The graph:

Piecewise:

The solution