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Solving integrals/ 1/sqrt(10-3x)

Integral of 1/sqrt(10-3x) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
  3                
  /                
 |                 
 |       1         
 |  ------------ dx
 |    __________   
 |  \/ 10 - 3*x    
 |                 
/                  
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∫133110−3x dx\int\limits_{\frac{1}{3}}^{3} \frac{1}{\sqrt{10 - 3 x}}\, dx 
Integral(1/(sqrt(10 - 3*x)), (x, 1/3, 3))
Detail solution

  1. Let u=10−3xu = \sqrt{10 - 3 x}.

    Then let du=−3dx210−3xdu = - \frac{3 dx}{2 \sqrt{10 - 3 x}} and substitute −2du3- \frac{2 du}{3}:

    ∫(−23) du\int \left(- \frac{2}{3}\right)\, du

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

      False\text{False}

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

        ∫1 du=u\int 1\, du = u

      So, the result is: −2u3- \frac{2 u}{3}

    Now substitute uu back in:

    −210−3x3- \frac{2 \sqrt{10 - 3 x}}{3}

  2. Add the constant of integration:

    −210−3x3+constant- \frac{2 \sqrt{10 - 3 x}}{3}+ \mathrm{constant}

The answer is:

−210−3x3+constant- \frac{2 \sqrt{10 - 3 x}}{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                    
 |                           __________
 |      1                2*\/ 10 - 3*x 
 | ------------ dx = C - --------------
 |   __________                3       
 | \/ 10 - 3*x                         
 |                                     
/
∫110−3x dx=C−210−3x3\int \frac{1}{\sqrt{10 - 3 x}}\, dx = C - \frac{2 \sqrt{10 - 3 x}}{3}
Simplify
The graph
3.000.500.751.001.251.501.752.002.252.502.755-5
Plot the graph f(x)
The answer [src] 
4/3
43\frac{4}{3} 
=
= 
4/3
43\frac{4}{3} 
4/3
Numerical answer [src] 
1.33333333333333
1.33333333333333

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

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