Integral of t^2 dx

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$$\int\limits_{0}^{1} t^{2}\, dt$$

Integral(t^2, (t, 0, 1))

Detail solution

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

$\int t^{2}\, dt = \frac{t^{3}}{3}$
Add the constant of integration:

$\frac{t^{3}}{3}+ \mathrm{constant}$

The answer is:

$\frac{t^{3}}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /              
 |              3
 |  2          t 
 | t  dt = C + --
 |             3 
/

$$\int t^{2}\, dt = C + \frac{t^{3}}{3}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

1/3

$$\frac{1}{3}$$

1/3

$$\frac{1}{3}$$

1/3

Numerical answer [src]

0.333333333333333

0.333333333333333

The graph

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