Integral of sqrt(4-y) dy

The solution

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  4             
  /             
 |              
 |    _______   
 |  \/ 4 - y  dy
 |              
/               
0

$$\int\limits_{0}^{4} \sqrt{4 - y}\, dy$$

Integral(sqrt(4 - y), (y, 0, 4))

Detail solution

Let $u = 4 - y$ .

Then let $du = - dy$ and substitute $- du$ :

$\int \left(- \sqrt{u}\right)\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \sqrt{u}\, du = - \int \sqrt{u}\, du$
  1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int \sqrt{u}\, du = \frac{2 u^{\frac{3}{2}}}{3}$
  So, the result is: $- \frac{2 u^{\frac{3}{2}}}{3}$
Now substitute $u$ back in:

$- \frac{2 \left(4 - y\right)^{\frac{3}{2}}}{3}$
Add the constant of integration:

$- \frac{2 \left(4 - y\right)^{\frac{3}{2}}}{3}+ \mathrm{constant}$

The answer is:

$- \frac{2 \left(4 - y\right)^{\frac{3}{2}}}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                               
 |                             3/2
 |   _______          2*(4 - y)   
 | \/ 4 - y  dy = C - ------------
 |                         3      
/

$$\int \sqrt{4 - y}\, dy = C - \frac{2 \left(4 - y\right)^{\frac{3}{2}}}{3}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

16/3

$$\frac{16}{3}$$

16/3

$$\frac{16}{3}$$

16/3

Numerical answer [src]

5.33333333333333

5.33333333333333

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

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Integral of sqrt(4-y) dy

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The solution