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2x^2-1
Solving integrals/ 2x^2-1

Integral of 2x^2-1 dx

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

You have entered [src] 
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0
∫01(2x2−1) dx\int\limits_{0}^{1} \left(2 x^{2} - 1\right)\, dx 
Integral(2*x^2 - 1*1, (x, 0, 1))
Detail solution

  1. Integrate term-by-term:

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

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

      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}

      So, the result is: 2x33\frac{2 x^{3}}{3}

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

      ∫((−1)1) dx=−x\int \left(\left(-1\right) 1\right)\, dx = - x

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

  2. Add the constant of integration:

    2x33−x+constant\frac{2 x^{3}}{3} - x+ \mathrm{constant}

The answer is:

2x33−x+constant\frac{2 x^{3}}{3} - x+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                            
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 | /   2    \              2*x 
 | \2*x  - 1/ dx = C - x + ----
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/
2 x33−x{{2\,x^3}\over{3}}-x
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.902-2
Plot the graph f(x)
The answer [src] 
-1/3
−13-{{1}\over{3}} 
=
= 
-1/3
−13- \frac{1}{3}
Simplify
Numerical answer [src] 
-0.333333333333333
-0.333333333333333
The graph
Integral of 2x^2-1 dx

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

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