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Solving integrals/ -5x

Integral of -5x dx

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The solution

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∫01(−5x) dx\int\limits_{0}^{1} \left(- 5 x\right)\, dx 
Integral(-5*x, (x, 0, 1))
Detail solution

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

    ∫(−5x) dx=−5∫x dx\int \left(- 5 x\right)\, dx = - 5 \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: −5x22- \frac{5 x^{2}}{2}

  2. Add the constant of integration:

    −5x22+constant- \frac{5 x^{2}}{2}+ \mathrm{constant}

The answer is:

−5x22+constant- \frac{5 x^{2}}{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
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∫(−5x) dx=C−5x22\int \left(- 5 x\right)\, dx = C - \frac{5 x^{2}}{2}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.905-10
Plot the graph f(x)
The answer [src] 
-5/2
−52- \frac{5}{2} 
=
= 
-5/2
−52- \frac{5}{2} 
-5/2
Numerical answer [src] 
-2.5
-2.5
The graph
Integral of -5x dx

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

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