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-4*x
Solving integrals/ -4*x

Integral of -4*x dx

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

You have entered [src] 
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∫01(−4x) dx\int\limits_{0}^{1} \left(- 4 x\right)\, dx 
Integral(-4*x, (x, 0, 1))
Detail solution

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

    ∫(−4x) dx=−4∫x dx\int \left(- 4 x\right)\, dx = - 4 \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: −2x2- 2 x^{2}

  2. Add the constant of integration:

    −2x2+constant- 2 x^{2}+ \mathrm{constant}

The answer is:

−2x2+constant- 2 x^{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
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 | -4*x dx = C - 2*x 
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−2 x2-2\,x^2
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.905-5
Plot the graph f(x)
The answer [src] 
-2
−2-2 
=
= 
-2
−2-2
Simplify
Numerical answer [src] 
-2.0
-2.0
The graph
Integral of -4*x dx

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

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