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Solving integrals/ (2x^2-3)dx

Integral of (2x^2-3)dx dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
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3
∫3−2(2x2−3) dx\int\limits_{3}^{-2} \left(2 x^{2} - 3\right)\, dx 
Integral(2*x^2 - 3, (x, 3, -2))
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:

      ∫(−3) dx=−3x\int \left(-3\right)\, dx = - 3 x

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

  2. Now simplify:

    x(2x2−9)3\frac{x \left(2 x^{2} - 9\right)}{3}

  3. Add the constant of integration:

    x(2x2−9)3+constant\frac{x \left(2 x^{2} - 9\right)}{3}+ \mathrm{constant}

The answer is:

x(2x2−9)3+constant\frac{x \left(2 x^{2} - 9\right)}{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                              
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 | /   2    \                2*x 
 | \2*x  - 3/ dx = C - 3*x + ----
 |                            3  
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∫(2x2−3) dx=C+2x33−3x\int \left(2 x^{2} - 3\right)\, dx = C + \frac{2 x^{3}}{3} - 3 x
Simplify
The graph
-2.0-1.5-1.0-0.53.00.00.51.01.52.02.5-2020
Plot the graph f(x)
The answer [src] 
-25/3
−253- \frac{25}{3} 
=
= 
-25/3
−253- \frac{25}{3} 
-25/3
Numerical answer [src] 
-8.33333333333333
-8.33333333333333

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

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