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Solving integrals/ 2x^3-3x^2+1

Integral of 2x^3-3x^2+1 dx

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The solution

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∫01((2x3−3x2)+1) dx\int\limits_{0}^{1} \left(\left(2 x^{3} - 3 x^{2}\right) + 1\right)\, dx 
Integral(2*x^3 - 3*x^2 + 1, (x, 0, 1))
Detail solution

  1. Integrate term-by-term:

    1. Integrate term-by-term:

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

        ∫2x3 dx=2∫x3 dx\int 2 x^{3}\, dx = 2 \int x^{3}\, dx

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

          ∫x3 dx=x44\int x^{3}\, dx = \frac{x^{4}}{4}

        So, the result is: x42\frac{x^{4}}{2}

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

        ∫(−3x2) dx=−3∫x2 dx\int \left(- 3 x^{2}\right)\, dx = - 3 \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: −x3- x^{3}

      The result is: x42−x3\frac{x^{4}}{2} - x^{3}

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

      ∫1 dx=x\int 1\, dx = x

    The result is: x42−x3+x\frac{x^{4}}{2} - x^{3} + x

  2. Add the constant of integration:

    x42−x3+x+constant\frac{x^{4}}{2} - x^{3} + x+ \mathrm{constant}

The answer is:

x42−x3+x+constant\frac{x^{4}}{2} - x^{3} + x+ \mathrm{constant}

The answer (Indefinite) [src] 
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 | \2*x  - 3*x  + 1/ dx = C + x + -- - x 
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∫((2x3−3x2)+1) dx=C+x42−x3+x\int \left(\left(2 x^{3} - 3 x^{2}\right) + 1\right)\, dx = C + \frac{x^{4}}{2} - x^{3} + x
Simplify
The graph
-1.00-0.75-0.50-0.252.000.000.250.500.751.001.251.501.75-1010
Plot the graph f(x)
The answer [src] 
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12\frac{1}{2} 
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= 
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12\frac{1}{2} 
1/2
Numerical answer [src] 
0.5
0.5

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

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