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Solving integrals/ 7-x

Integral of 7-x dx

Limits of integration:

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The graph:

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Piecewise:

The solution

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∫04(7−x) dx\int\limits_{0}^{4} \left(7 - x\right)\, dx 
Integral(7 - x, (x, 0, 4))
Detail solution

  1. Integrate term-by-term:

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

      ∫7 dx=7x\int 7\, dx = 7 x

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

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

    The result is: −x22+7x- \frac{x^{2}}{2} + 7 x

  2. Now simplify:

    x(14−x)2\frac{x \left(14 - x\right)}{2}

  3. Add the constant of integration:

    x(14−x)2+constant\frac{x \left(14 - x\right)}{2}+ \mathrm{constant}

The answer is:

x(14−x)2+constant\frac{x \left(14 - x\right)}{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
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 | (7 - x) dx = C + 7*x - --
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∫(7−x) dx=C−x22+7x\int \left(7 - x\right)\, dx = C - \frac{x^{2}}{2} + 7 x
Simplify
The graph
0.04.00.51.01.52.02.53.03.5040
Plot the graph f(x)
The answer [src] 
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Numerical answer [src] 
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    Use the examples entering the upper and lower limits of integration.

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