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Solving integrals/ y^(1/2)

Integral of y^(1/2) dx

You have entered [src]

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

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

Integral(sqrt(y), (y, 0, 1))

Detail solution

The integral of $y^{n}$ is $\frac{y^{n + 1}}{n + 1}$ when $n \neq -1$ :

$\int \sqrt{y}\, dy = \frac{2 y^{\frac{3}{2}}}{3}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

2/3

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

2/3

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

2/3

Numerical answer [src]

0.666666666666667

0.666666666666667

The graph

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