Mister Exam

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Identical expressions
sqrt(y+ one)
square root of (y plus 1)
square root of (y plus one)
√(y+1)
sqrty+1
Similar expressions
(y-1)/(sqrty+1)
ln((sqrty)+1)
sqrt(y-1)

Integral of sqrt(y+1) dy

The solution

You have entered [src]

  1             
  /             
 |              
 |    _______   
 |  \/ y + 1  dy
 |              
/               
0

$$\int\limits_{0}^{1} \sqrt{y + 1}\, dy$$

Integral(sqrt(y + 1), (y, 0, 1))

Detail solution

Let $u = y + 1$ .

Then let $du = dy$ 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:

$\frac{2 \left(y + 1\right)^{\frac{3}{2}}}{3}$
Now simplify:

$\frac{2 \left(y + 1\right)^{\frac{3}{2}}}{3}$
Add the constant of integration:

$\frac{2 \left(y + 1\right)^{\frac{3}{2}}}{3}+ \mathrm{constant}$

The answer is:

$\frac{2 \left(y + 1\right)^{\frac{3}{2}}}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                               
 |                             3/2
 |   _______          2*(y + 1)   
 | \/ y + 1  dy = C + ------------
 |                         3      
/

$$\int \sqrt{y + 1}\, dy = C + \frac{2 \left(y + 1\right)^{\frac{3}{2}}}{3}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

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

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

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

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

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

Numerical answer [src]

1.21895141649746

1.21895141649746

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

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Identical expressions

Similar expressions

Integral of sqrt(y+1) dy

Limits of integration:

The graph:

Piecewise:

The solution