Mister Exam

Other calculators

Solving integrals/ x^2-x+1

Integral of x^2-x+1 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  0                
  /                
 |                 
 |  / 2        \   
 |  \x  - x + 1/ dx
 |                 
/                  
-1
$$\int\limits_{-1}^{0} \left(\left(x^{2} - x\right) + 1\right)\, dx$$ 
Integral(x^2 - x + 1, (x, -1, 0))
Detail solution

  1. Integrate term-by-term:

    1. Integrate term-by-term:

      1. The integral of is when :

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

        1. The integral of is when :

        So, the result is:

      The result is:

    1. The integral of a constant is the constant times the variable of integration:

    The result is:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                 
 |                            2    3
 | / 2        \              x    x 
 | \x  - x + 1/ dx = C + x - -- + --
 |                           2    3 
/
$$\int \left(\left(x^{2} - x\right) + 1\right)\, dx = C + \frac{x^{3}}{3} - \frac{x^{2}}{2} + x$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
11/6
$$\frac{11}{6}$$ 
=
= 
11/6
$$\frac{11}{6}$$ 
11/6
Numerical answer [src] 
1.83333333333333
1.83333333333333

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

    © Mister Exam – Calculator