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sqrt(5-2x)
Solving integrals/ sqrt(5-2x)

Integral of sqrt(5-2x) dx

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The graph:

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The solution

You have entered [src] 
  1               
  /               
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 |    _________   
 |  \/ 5 - 2*x  dx
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0
∫015−2x dx\int\limits_{0}^{1} \sqrt{5 - 2 x}\, dx 
Integral(sqrt(5 - 2*x), (x, 0, 1))
Detail solution

  1. Let u=5−2xu = 5 - 2 x.

    Then let du=−2dxdu = - 2 dx and substitute −du2- \frac{du}{2}:

    ∫(−u2) du\int \left(- \frac{\sqrt{u}}{2}\right)\, du

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

      ∫u du=−∫u du2\int \sqrt{u}\, du = - \frac{\int \sqrt{u}\, du}{2}

      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: −u323- \frac{u^{\frac{3}{2}}}{3}

    Now substitute uu back in:

    −(5−2x)323- \frac{\left(5 - 2 x\right)^{\frac{3}{2}}}{3}

  2. Add the constant of integration:

    −(5−2x)323+constant- \frac{\left(5 - 2 x\right)^{\frac{3}{2}}}{3}+ \mathrm{constant}

The answer is:

−(5−2x)323+constant- \frac{\left(5 - 2 x\right)^{\frac{3}{2}}}{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                 
 |                               3/2
 |   _________          (5 - 2*x)   
 | \/ 5 - 2*x  dx = C - ------------
 |                           3      
/
∫5−2x dx=C−(5−2x)323\int \sqrt{5 - 2 x}\, dx = C - \frac{\left(5 - 2 x\right)^{\frac{3}{2}}}{3}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.905-5
Plot the graph f(x)
The answer [src] 
              ___
    ___   5*\/ 5 
- \/ 3  + -------
             3
−3+553- \sqrt{3} + \frac{5 \sqrt{5}}{3} 
=
= 
              ___
    ___   5*\/ 5 
- \/ 3  + -------
             3
−3+553- \sqrt{3} + \frac{5 \sqrt{5}}{3} 
-sqrt(3) + 5*sqrt(5)/3
Numerical answer [src] 
1.99472915493077
1.99472915493077
The graph
Integral of sqrt(5-2x) dx

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

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