Integral of sinx+1 dx

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$$\int\limits_{0}^{1} \left(\sin{\left(x \right)} + 1\right)\, dx$$

Integral(sin(x) + 1, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of sine is negative cosine:
  
  $\int \sin{\left(x \right)}\, dx = - \cos{\left(x \right)}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 1\, dx = x$
The result is: $x - \cos{\left(x \right)}$
Add the constant of integration:

$x - \cos{\left(x \right)}+ \mathrm{constant}$

The answer is:

$x - \cos{\left(x \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

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 | (sin(x) + 1) dx = C + x - cos(x)
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$$\int \left(\sin{\left(x \right)} + 1\right)\, dx = C + x - \cos{\left(x \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

2 - cos(1)

$$2 - \cos{\left(1 \right)}$$

2 - cos(1)

$$2 - \cos{\left(1 \right)}$$

2 - cos(1)

Numerical answer [src]

1.45969769413186

1.45969769413186

The graph

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