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Solving integrals/ sin(pi*x/4)

Integral of sin(pi*x/4) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

  1. Let .

    Then let and substitute :

    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:

    Now substitute back in:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                        /pi*x\
 |                    4*cos|----|
 |    /pi*x\               \ 4  /
 | sin|----| dx = C - -----------
 |    \ 4  /               pi    
 |                               
/
$$\int \sin{\left(\frac{\pi x}{4} \right)}\, dx = C - \frac{4 \cos{\left(\frac{\pi x}{4} \right)}}{\pi}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
8 
--
pi
$$\frac{8}{\pi}$$ 
=
= 
8 
--
pi
$$\frac{8}{\pi}$$ 
8/pi
Numerical answer [src] 
2.54647908947033
2.54647908947033

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

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