Mister Exam

Lang:

Solving integrals/ y^(2/3)

Integral of y^(2/3) dx

You have entered [src]

$$\int\limits_{0}^{8} y^{\frac{2}{3}}\, dy$$

Integral(y^(2/3), (y, 0, 8))

Detail solution

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

$\int y^{\frac{2}{3}}\, dy = \frac{3 y^{\frac{5}{3}}}{5}$
Add the constant of integration:

$\frac{3 y^{\frac{5}{3}}}{5}+ \mathrm{constant}$

The answer is:

$\frac{3 y^{\frac{5}{3}}}{5}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                    
 |                  5/3
 |  2/3          3*y   
 | y    dy = C + ------
 |                 5   
/

$$\int y^{\frac{2}{3}}\, dy = C + \frac{3 y^{\frac{5}{3}}}{5}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

96/5

$$\frac{96}{5}$$

96/5

$$\frac{96}{5}$$

96/5

Numerical answer [src]

19.2

19.2

The graph

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