Integral of sin-1(x) dx

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

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

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- x\right)\, dx = - \int x\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x\, dx = \frac{x^{2}}{2}$
  So, the result is: $- \frac{x^{2}}{2}$
1. The integral of sine is negative cosine:
  
  $\int \sin{\left(x \right)}\, dx = - \cos{\left(x \right)}$
The result is: $- \frac{x^{2}}{2} - \cos{\left(x \right)}$
Add the constant of integration:

$- \frac{x^{2}}{2} - \cos{\left(x \right)}+ \mathrm{constant}$

The answer is:

$- \frac{x^{2}}{2} - \cos{\left(x \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                2
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 | (sin(x) - x) dx = C - cos(x) - --
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$$\int \left(- x + \sin{\left(x \right)}\right)\, dx = C - \frac{x^{2}}{2} - \cos{\left(x \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

1/2 - cos(1)

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

1/2 - cos(1)

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

1/2 - cos(1)

Numerical answer [src]

-0.0403023058681397

-0.0403023058681397

The graph

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