Mister Exam

Other calculators

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

Integral of cos(x)-1 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                
  /                
 |                 
 |  (cos(x) - 1) dx
 |                 
/                  
0
∫01(cos⁡(x)−1) dx\int\limits_{0}^{1} \left(\cos{\left(x \right)} - 1\right)\, dx 
Integral(cos(x) - 1, (x, 0, 1))
Detail solution

  1. Integrate term-by-term:

    1. The integral of cosine is sine:

      ∫cos⁡(x) dx=sin⁡(x)\int \cos{\left(x \right)}\, dx = \sin{\left(x \right)}

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

      ∫(−1) dx=−x\int \left(-1\right)\, dx = - x

    The result is: −x+sin⁡(x)- x + \sin{\left(x \right)}

  2. Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src] 
  /                                
 |                                 
 | (cos(x) - 1) dx = C - x + sin(x)
 |                                 
/
∫(cos⁡(x)−1) dx=C−x+sin⁡(x)\int \left(\cos{\left(x \right)} - 1\right)\, dx = C - x + \sin{\left(x \right)}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.900.5-0.5
Plot the graph f(x)
The answer [src] 
-1 + sin(1)
−1+sin⁡(1)-1 + \sin{\left(1 \right)} 
=
= 
-1 + sin(1)
−1+sin⁡(1)-1 + \sin{\left(1 \right)} 
-1 + sin(1)
Numerical answer [src] 
-0.158529015192103
-0.158529015192103
The graph
Integral of cos(x)-1 dx

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

    © Mister Exam – Calculator