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(-1)^x
Solving integrals/ (-1)^x

Integral of (-1)^x dx

Limits of integration:

from to
v

The graph:

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Piecewise:

The solution

You have entered [src] 
  1         
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 |      x   
 |  (-1)  dx
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0
∫01(−1)x dx\int\limits_{0}^{1} \left(-1\right)^{x}\, dx 
Integral((-1)^x, (x, 0, 1))
Detail solution

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

    ∫(−1)x dx=−(−1)xiπ\int \left(-1\right)^{x}\, dx = - \frac{\left(-1\right)^{x} i}{\pi}

  2. Now simplify:

    (−1)x+32π\frac{\left(-1\right)^{x + \frac{3}{2}}}{\pi}

  3. Add the constant of integration:

    (−1)x+32π+constant\frac{\left(-1\right)^{x + \frac{3}{2}}}{\pi}+ \mathrm{constant}

The answer is:

(−1)x+32π+constant\frac{\left(-1\right)^{x + \frac{3}{2}}}{\pi}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                      
 |                      x
 |     x          I*(-1) 
 | (-1)  dx = C - -------
 |                   pi  
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∫(−1)x dx=−(−1)xiπ+C\int \left(-1\right)^{x}\, dx = - \frac{\left(-1\right)^{x} i}{\pi} + C
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.902-2
Plot the graph f(x)
The answer [src] 
2*I
---
 pi
2iπ\frac{2 i}{\pi} 
=
= 
2*I
---
 pi
2iπ\frac{2 i}{\pi} 
2*i/pi
Numerical answer [src] 
(6.22746185175318e-24 + 0.636619772367581j)
(6.22746185175318e-24 + 0.636619772367581j)
The graph
Integral of (-1)^x dx

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

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