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Solving integrals/ 3sinx/3

Integral of 3sinx/3 dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
 3*pi           
 ----           
  2             
   /            
  |             
  |  3*sin(x)   
  |  -------- dx
  |     3       
  |             
 /              
 0
∫03π23sin⁡(x)3 dx\int\limits_{0}^{\frac{3 \pi}{2}} \frac{3 \sin{\left(x \right)}}{3}\, dx 
Integral((3*sin(x))/3, (x, 0, 3*pi/2))
Detail solution

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

    ∫3sin⁡(x)3 dx=∫3sin⁡(x) dx3\int \frac{3 \sin{\left(x \right)}}{3}\, dx = \frac{\int 3 \sin{\left(x \right)}\, dx}{3}

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

      ∫3sin⁡(x) dx=3∫sin⁡(x) dx\int 3 \sin{\left(x \right)}\, dx = 3 \int \sin{\left(x \right)}\, dx

      1. Don't know the steps in finding this integral.

        But the integral is

        −cos⁡(x)- \cos{\left(x \right)}

      So, the result is: −3cos⁡(x)- 3 \cos{\left(x \right)}

    So, the result is: −cos⁡(x)- \cos{\left(x \right)}

  2. Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src] 
  /                        
 |                         
 | 3*sin(x)                
 | -------- dx = C - cos(x)
 |    3                    
 |                         
/
∫3sin⁡(x)3 dx=C−cos⁡(x)\int \frac{3 \sin{\left(x \right)}}{3}\, dx = C - \cos{\left(x \right)}
Simplify
The graph
0.00.51.01.52.02.53.03.54.04.52-2
Plot the graph f(x)
The answer [src] 
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11 
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11 
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Numerical answer [src] 
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    Use the examples entering the upper and lower limits of integration.

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