Mister Exam

Other calculators

x^2-2
Solving integrals/ x^2-2

Integral of x^2-2 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1            
  /            
 |             
 |  / 2    \   
 |  \x  - 2/ dx
 |             
/              
0
∫01(x2−2) dx\int\limits_{0}^{1} \left(x^{2} - 2\right)\, dx 
Integral(x^2 - 2, (x, 0, 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 is the constant times the variable of integration:

      ∫(−2) dx=−2x\int \left(-2\right)\, dx = - 2 x

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

  2. Now simplify:

    x(x2−6)3\frac{x \left(x^{2} - 6\right)}{3}

  3. Add the constant of integration:

    x(x2−6)3+constant\frac{x \left(x^{2} - 6\right)}{3}+ \mathrm{constant}

The answer is:

x(x2−6)3+constant\frac{x \left(x^{2} - 6\right)}{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                          
 |                          3
 | / 2    \                x 
 | \x  - 2/ dx = C - 2*x + --
 |                         3 
/
∫(x2−2) dx=C+x33−2x\int \left(x^{2} - 2\right)\, dx = C + \frac{x^{3}}{3} - 2 x
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.902-4
Plot the graph f(x)
The answer [src] 
-5/3
−53- \frac{5}{3} 
=
= 
-5/3
−53- \frac{5}{3} 
-5/3
Numerical answer [src] 
-1.66666666666667
-1.66666666666667
The graph
Integral of x^2-2 dx

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

    © Mister Exam – Calculator