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Solving integrals/ sinx/4

Integral of sinx/4 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 pi          
  /          
 |           
 |  sin(x)   
 |  ------ dx
 |    4      
 |           
/            
0
∫0πsin⁡(x)4 dx\int\limits_{0}^{\pi} \frac{\sin{\left(x \right)}}{4}\, dx 
Integral(sin(x)/4, (x, 0, pi))
Detail solution

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

    ∫sin⁡(x)4 dx=∫sin⁡(x) dx4\int \frac{\sin{\left(x \right)}}{4}\, dx = \frac{\int \sin{\left(x \right)}\, dx}{4}

    1. The integral of sine is negative cosine:

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

    So, the result is: −cos⁡(x)4- \frac{\cos{\left(x \right)}}{4}

  2. Add the constant of integration:

    −cos⁡(x)4+constant- \frac{\cos{\left(x \right)}}{4}+ \mathrm{constant}

The answer is:

−cos⁡(x)4+constant- \frac{\cos{\left(x \right)}}{4}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                      
 |                       
 | sin(x)          cos(x)
 | ------ dx = C - ------
 |   4               4   
 |                       
/
∫sin⁡(x)4 dx=C−cos⁡(x)4\int \frac{\sin{\left(x \right)}}{4}\, dx = C - \frac{\cos{\left(x \right)}}{4}
Simplify
The graph
0.000.250.500.751.001.251.501.752.002.252.502.753.000.5-0.5
Plot the graph f(x)
The answer [src] 
1/2
12\frac{1}{2} 
=
= 
1/2
12\frac{1}{2} 
1/2
Numerical answer [src] 
0.5
0.5

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

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