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Graphing y =:
(x-3)^1/2
Identical expressions
(x- three)^ one / two
(x minus 3) to the power of 1 divide by 2
(x minus three) to the power of one divide by two
(x-3)1/2
x-31/2
x-3^1/2
(x-3)^1 divide by 2
(x-3)^1/2dx
Similar expressions
(x+3)^1/2

Solving integrals/ (x-3)^1/2

Integral of (x-3)^1/2 dx

The solution

You have entered [src]

  1             
  /             
 |              
 |    _______   
 |  \/ x - 3  dx
 |              
/               
0

$$\int\limits_{0}^{1} \sqrt{x - 3}\, dx$$

Integral(sqrt(x - 3), (x, 0, 1))

Detail solution

Let $u = x - 3$ .

Then let $du = dx$ and substitute $du$ :

$\int \sqrt{u}\, du$
1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int \sqrt{u}\, du = \frac{2 u^{\frac{3}{2}}}{3}$
Now substitute $u$ back in:

$\frac{2 \left(x - 3\right)^{\frac{3}{2}}}{3}$
Now simplify:

$\frac{2 \left(x - 3\right)^{\frac{3}{2}}}{3}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

  /                               
 |                             3/2
 |   _______          2*(x - 3)   
 | \/ x - 3  dx = C + ------------
 |                         3      
/

$$\int \sqrt{x - 3}\, dx = C + \frac{2 \left(x - 3\right)^{\frac{3}{2}}}{3}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

                  ___
      ___   4*I*\/ 2 
2*I*\/ 3  - ---------
                3

$$- \frac{4 \sqrt{2} i}{3} + 2 \sqrt{3} i$$

                  ___
      ___   4*I*\/ 2 
2*I*\/ 3  - ---------
                3

$$- \frac{4 \sqrt{2} i}{3} + 2 \sqrt{3} i$$

2*i*sqrt(3) - 4*i*sqrt(2)/3

Numerical answer [src]

(0.0 + 1.57848353197363j)

(0.0 + 1.57848353197363j)

The graph

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

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Identical expressions

Similar expressions

Integral of (x-3)^1/2 dx

Limits of integration:

The graph:

Piecewise:

The solution