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Solving integrals/ 5x^2-20

Integral of 5x^2-20 dx

Limits of integration:

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The graph:

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Piecewise:

The solution

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∫−21(5x2−20) dx\int\limits_{-2}^{1} \left(5 x^{2} - 20\right)\, dx 
Integral(5*x^2 - 20, (x, -2, 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:

      ∫5x2 dx=5∫x2 dx\int 5 x^{2}\, dx = 5 \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: 5x33\frac{5 x^{3}}{3}

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

      ∫(−20) dx=−20x\int \left(-20\right)\, dx = - 20 x

    The result is: 5x33−20x\frac{5 x^{3}}{3} - 20 x

  2. Now simplify:

    5x(x2−12)3\frac{5 x \left(x^{2} - 12\right)}{3}

  3. Add the constant of integration:

    5x(x2−12)3+constant\frac{5 x \left(x^{2} - 12\right)}{3}+ \mathrm{constant}

The answer is:

5x(x2−12)3+constant\frac{5 x \left(x^{2} - 12\right)}{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
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 | \5*x  - 20/ dx = C - 20*x + ----
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∫(5x2−20) dx=C+5x33−20x\int \left(5 x^{2} - 20\right)\, dx = C + \frac{5 x^{3}}{3} - 20 x
Simplify
The graph
-2.00-1.75-1.50-1.25-1.00-0.75-0.50-0.251.000.000.250.500.75-5050
Plot the graph f(x)
The answer [src] 
-45
−45-45 
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-45
−45-45 
-45
Numerical answer [src] 
-45.0
-45.0

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

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