Integral of cos(x)-1 dx

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

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

Detail solution

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

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

The answer is:

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

The answer (Indefinite) [src]

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

-1 + sin(1)

$$-1 + \sin{\left(1 \right)}$$

-1 + sin(1)

$$-1 + \sin{\left(1 \right)}$$

-1 + sin(1)

Numerical answer [src]

-0.158529015192103

-0.158529015192103

The graph

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