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x^2-3x+4
Solving integrals/ x^2-3x+4

Integral of x^2-3x+4 dx

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The solution

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∫01((x2−3x)+4) dx\int\limits_{0}^{1} \left(\left(x^{2} - 3 x\right) + 4\right)\, dx 
Integral(x^2 - 3*x + 4, (x, 0, 1))
Detail solution

  1. Integrate term-by-term:

    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 times a function is the constant times the integral of the function:

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

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

          ∫x dx=x22\int x\, dx = \frac{x^{2}}{2}

        So, the result is: −3x22- \frac{3 x^{2}}{2}

      The result is: x33−3x22\frac{x^{3}}{3} - \frac{3 x^{2}}{2}

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

      ∫4 dx=4x\int 4\, dx = 4 x

    The result is: x33−3x22+4x\frac{x^{3}}{3} - \frac{3 x^{2}}{2} + 4 x

  2. Now simplify:

    x(2x2−9x+24)6\frac{x \left(2 x^{2} - 9 x + 24\right)}{6}

  3. Add the constant of integration:

    x(2x2−9x+24)6+constant\frac{x \left(2 x^{2} - 9 x + 24\right)}{6}+ \mathrm{constant}

The answer is:

x(2x2−9x+24)6+constant\frac{x \left(2 x^{2} - 9 x + 24\right)}{6}+ \mathrm{constant}

The answer (Indefinite) [src] 
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 | \x  - 3*x + 4/ dx = C + 4*x - ---- + --
 |                                2     3 
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∫((x2−3x)+4) dx=C+x33−3x22+4x\int \left(\left(x^{2} - 3 x\right) + 4\right)\, dx = C + \frac{x^{3}}{3} - \frac{3 x^{2}}{2} + 4 x
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.9005
Plot the graph f(x)
The answer [src] 
17/6
176\frac{17}{6} 
=
= 
17/6
176\frac{17}{6} 
17/6
Numerical answer [src] 
2.83333333333333
2.83333333333333
The graph
Integral of x^2-3x+4 dx

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

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