Integral of x-sinx dx

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

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

Detail solution

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

-1/2 + cos(1)

$${{2\,\cos 1-1}\over{2}}$$

-1/2 + cos(1)

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

Simplify

Numerical answer [src]

0.0403023058681397

0.0403023058681397

The graph

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