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Solving integrals/ -5x^2

Integral of -5x^2 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
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∫01(−5x2) dx\int\limits_{0}^{1} \left(- 5 x^{2}\right)\, dx 
Integral(-5*x^2, (x, 0, 1))
Detail solution

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

    ∫(−5x2) dx=−5∫x2 dx\int \left(- 5 x^{2}\right)\, 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}

  2. Add the constant of integration:

    −5x33+constant- \frac{5 x^{3}}{3}+ \mathrm{constant}

The answer is:

−5x33+constant- \frac{5 x^{3}}{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                   
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 |     2          5*x 
 | -5*x  dx = C - ----
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∫(−5x2) dx=C−5x33\int \left(- 5 x^{2}\right)\, dx = C - \frac{5 x^{3}}{3}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.905-10
Plot the graph f(x)
The answer [src] 
-5/3
−53- \frac{5}{3} 
=
= 
-5/3
−53- \frac{5}{3} 
-5/3
Numerical answer [src] 
-1.66666666666667
-1.66666666666667

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

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