Mister Exam

Other calculators

-x
Solving integrals/ -x

Integral of -x dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

  1. The integral of a constant times a function is the constant times the integral of the function:

    ∫(−x) dx=−∫x dx\int \left(- x\right)\, dx = - \int x\, dx

    1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n≠−1n \neq -1:

      ∫x dx=x22\int x\, dx = \frac{x^{2}}{2}

    So, the result is: −x22- \frac{x^{2}}{2}

  2. Add the constant of integration:

    −x22+constant- \frac{x^{2}}{2}+ \mathrm{constant}

The answer is:

−x22+constant- \frac{x^{2}}{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /             2
 |             x 
 | -x dx = C - --
 |             2 
/
∫(−x) dx=C−x22\int \left(- x\right)\, dx = C - \frac{x^{2}}{2}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.901-2
Plot the graph f(x)
The answer [src] 
-1/2
−12- \frac{1}{2} 
=
= 
-1/2
−12- \frac{1}{2} 
-1/2
Numerical answer [src] 
-0.5
-0.5
The graph
Integral of -x dx

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

    © Mister Exam – Calculator