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Solving integrals/ -3x

Integral of -3x dx

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The solution

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

  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}

  2. Add the constant of integration:

    −3x22+constant- \frac{3 x^{2}}{2}+ \mathrm{constant}

The answer is:

−3x22+constant- \frac{3 x^{2}}{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
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∫(−3x) dx=C−3x22\int \left(- 3 x\right)\, dx = C - \frac{3 x^{2}}{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] 
-3/2
−32- \frac{3}{2} 
=
= 
-3/2
−32- \frac{3}{2} 
-3/2
Numerical answer [src] 
-1.5
-1.5
The graph
Integral of -3x dx

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

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