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Solving integrals/ 1-sin(x)-cos(x)

Integral of 1-sin(x)-cos(x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                         
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 |  (1 - sin(x) - cos(x)) dx
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0
$$\int\limits_{0}^{1} \left(\left(1 - \sin{\left(x \right)}\right) - \cos{\left(x \right)}\right)\, dx$$ 
Integral(1 - sin(x) - cos(x), (x, 0, 1))
Detail solution

  1. Integrate term-by-term:

    1. Integrate term-by-term:

      1. The integral of a constant is the constant times the variable of integration:

      1. The integral of a constant times a function is the constant times the integral of the function:

        1. The integral of sine is negative cosine:

        So, the result is:

      The result is:

    1. The integral of a constant times a function is the constant times the integral of the function:

      1. The integral of cosine is sine:

      So, the result is:

    The result is:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                                  
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 | (1 - sin(x) - cos(x)) dx = C + x - sin(x) + cos(x)
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$$\int \left(\left(1 - \sin{\left(x \right)}\right) - \cos{\left(x \right)}\right)\, dx = C + x - \sin{\left(x \right)} + \cos{\left(x \right)}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
-sin(1) + cos(1)
$$- \sin{\left(1 \right)} + \cos{\left(1 \right)}$$ 
=
= 
-sin(1) + cos(1)
$$- \sin{\left(1 \right)} + \cos{\left(1 \right)}$$ 
-sin(1) + cos(1)
Numerical answer [src] 
-0.301168678939757
-0.301168678939757

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

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