Mister Exam

Lang:

Integral of z^3 dz

You have entered [src]

$$\int\limits_{0}^{1 + i} z^{3}\, dz$$

Integral(z^3, (z, 0, 1 + i))

Detail solution

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

$\int z^{3}\, dz = \frac{z^{4}}{4}$
Add the constant of integration:

$\frac{z^{4}}{4}+ \mathrm{constant}$

The answer is:

$\frac{z^{4}}{4}+ \mathrm{constant}$

The answer [src]

       4
(1 + I) 
--------
   4

$$\frac{\left(1 + i\right)^{4}}{4}$$

       4
(1 + I) 
--------
   4

$$\frac{\left(1 + i\right)^{4}}{4}$$

(1 + i)^4/4

Numerical answer [src]

(-1.0 + 0.0j)

(-1.0 + 0.0j)

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