Integral of t+1 dx

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$$\int\limits_{0}^{1} \left(t + 1\right)\, dt$$

Integral(t + 1, (t, 0, 1))

Detail solution

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

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

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

The answer is:

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

The answer (Indefinite) [src]

  /                      2
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 | (t + 1) dt = C + t + --
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$$\int \left(t + 1\right)\, dt = C + \frac{t^{2}}{2} + t$$

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.