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sqrt(1-x)
Solving integrals/ sqrt(1-x)

Integral of sqrt(1-x) dx

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The solution

You have entered [src] 
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∫011−x dx\int\limits_{0}^{1} \sqrt{1 - x}\, dx 
Integral(sqrt(1 - x), (x, 0, 1))
Detail solution

  1. Let u=1−xu = 1 - x.

    Then let du=−dxdu = - dx and substitute −du- du:

    ∫(−u) du\int \left(- \sqrt{u}\right)\, du

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

      ∫u du=−∫u du\int \sqrt{u}\, du = - \int \sqrt{u}\, du

      1. The integral of unu^{n} is un+1n+1\frac{u^{n + 1}}{n + 1} when n≠−1n \neq -1:

        ∫u du=2u323\int \sqrt{u}\, du = \frac{2 u^{\frac{3}{2}}}{3}

      So, the result is: −2u323- \frac{2 u^{\frac{3}{2}}}{3}

    Now substitute uu back in:

    −2(1−x)323- \frac{2 \left(1 - x\right)^{\frac{3}{2}}}{3}

  2. Add the constant of integration:

    −2(1−x)323+constant- \frac{2 \left(1 - x\right)^{\frac{3}{2}}}{3}+ \mathrm{constant}

The answer is:

−2(1−x)323+constant- \frac{2 \left(1 - x\right)^{\frac{3}{2}}}{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
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∫1−x dx=C−2(1−x)323\int \sqrt{1 - x}\, dx = C - \frac{2 \left(1 - x\right)^{\frac{3}{2}}}{3}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.902-2
Plot the graph f(x)
The answer [src] 
2/3
23\frac{2}{3} 
=
= 
2/3
23\frac{2}{3} 
2/3
Numerical answer [src] 
0.666666666666667
0.666666666666667
The graph
Integral of sqrt(1-x) dx

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

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