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Solving integrals/ (-1)^x

Integral of (-1)^x dx

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  1         
  /         
 |          
 |      x   
 |  (-1)  dx
 |          
/           
0

$$\int\limits_{0}^{1} \left(-1\right)^{x}\, dx$$

Integral((-1)^x, (x, 0, 1))

Detail solution

The integral of an exponential function is itself divided by the natural logarithm of the base.

$\int \left(-1\right)^{x}\, dx = - \frac{\left(-1\right)^{x} i}{\pi}$
Now simplify:

$\frac{\left(-1\right)^{x + \frac{3}{2}}}{\pi}$
Add the constant of integration:

$\frac{\left(-1\right)^{x + \frac{3}{2}}}{\pi}+ \mathrm{constant}$

The answer is:

$\frac{\left(-1\right)^{x + \frac{3}{2}}}{\pi}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                      
 |                      x
 |     x          I*(-1) 
 | (-1)  dx = C - -------
 |                   pi  
/

$$\int \left(-1\right)^{x}\, dx = - \frac{\left(-1\right)^{x} i}{\pi} + C$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

2*I
---
 pi

$$\frac{2 i}{\pi}$$

2*I
---
 pi

$$\frac{2 i}{\pi}$$

2*i/pi

Numerical answer [src]

(6.22746185175318e-24 + 0.636619772367581j)

(6.22746185175318e-24 + 0.636619772367581j)

The graph

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