Integral of 1+y dy

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$$\int\limits_{0}^{1} \left(y + 1\right)\, dy$$

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

Detail solution

Integrate term-by-term:
1. The integral of $y^{n}$ is $\frac{y^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int y\, dy = \frac{y^{2}}{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 1\, dy = y$
The result is: $\frac{y^{2}}{2} + y$
Now simplify:

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

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

The answer is:

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

The answer (Indefinite) [src]

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

3/2

$$\frac{3}{2}$$

3/2

$$\frac{3}{2}$$

3/2

Numerical answer [src]

1.5

1.5

The graph

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