Mister Exam

Other calculators

Solving integrals/ x^2-2*x

Integral of x^2-2*x dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1              
  /              
 |               
 |  / 2      \   
 |  \x  - 2*x/ dx
 |               
/                
-2
∫−21(x2−2x) dx\int\limits_{-2}^{1} \left(x^{2} - 2 x\right)\, dx 
Integral(x^2 - 2*x, (x, -2, 1))
Detail solution

  1. Integrate term-by-term:

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

      ∫x2 dx=x33\int x^{2}\, dx = \frac{x^{3}}{3}

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

      ∫(−2x) dx=−2∫x dx\int \left(- 2 x\right)\, dx = - 2 \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: −x2- x^{2}

    The result is: x33−x2\frac{x^{3}}{3} - x^{2}

  2. Now simplify:

    x2(x−3)3\frac{x^{2} \left(x - 3\right)}{3}

  3. Add the constant of integration:

    x2(x−3)3+constant\frac{x^{2} \left(x - 3\right)}{3}+ \mathrm{constant}

The answer is:

x2(x−3)3+constant\frac{x^{2} \left(x - 3\right)}{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                           
 |                           3
 | / 2      \           2   x 
 | \x  - 2*x/ dx = C - x  + --
 |                          3 
/
∫(x2−2x) dx=C+x33−x2\int \left(x^{2} - 2 x\right)\, dx = C + \frac{x^{3}}{3} - x^{2}
Simplify
The graph
-2.00-1.75-1.50-1.25-1.00-0.75-0.50-0.251.000.000.250.500.75-2020
Plot the graph f(x)
The answer [src] 
6
66 
=
= 
6
66 
6
Numerical answer [src] 
6.0
6.0

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

    © Mister Exam – Calculator