Mister Exam

Other calculators

sin(x/4)dx
Solving integrals/ sin(x/4)dx

Integral of sin(x/4)dx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1          
  /          
 |           
 |     /x\   
 |  sin|-| dx
 |     \4/   
 |           
/            
0
∫01sin⁡(x4) dx\int\limits_{0}^{1} \sin{\left(\frac{x}{4} \right)}\, dx 
Integral(sin(x/4), (x, 0, 1))
Detail solution

  1. Let u=x4u = \frac{x}{4}.

    Then let du=dx4du = \frac{dx}{4} and substitute 4du4 du:

    ∫4sin⁡(u) du\int 4 \sin{\left(u \right)}\, du

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

      ∫sin⁡(u) du=4∫sin⁡(u) du\int \sin{\left(u \right)}\, du = 4 \int \sin{\left(u \right)}\, du

      1. The integral of sine is negative cosine:

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

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

    Now substitute uu back in:

    −4cos⁡(x4)- 4 \cos{\left(\frac{x}{4} \right)}

  2. Now simplify:

    −4cos⁡(x4)- 4 \cos{\left(\frac{x}{4} \right)}

  3. Add the constant of integration:

    −4cos⁡(x4)+constant- 4 \cos{\left(\frac{x}{4} \right)}+ \mathrm{constant}

The answer is:

−4cos⁡(x4)+constant- 4 \cos{\left(\frac{x}{4} \right)}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                        
 |                         
 |    /x\               /x\
 | sin|-| dx = C - 4*cos|-|
 |    \4/               \4/
 |                         
/
∫sin⁡(x4) dx=C−4cos⁡(x4)\int \sin{\left(\frac{x}{4} \right)}\, dx = C - 4 \cos{\left(\frac{x}{4} \right)}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.905-5
Plot the graph f(x)
The answer [src] 
4 - 4*cos(1/4)
4−4cos⁡(14)4 - 4 \cos{\left(\frac{1}{4} \right)} 
=
= 
4 - 4*cos(1/4)
4−4cos⁡(14)4 - 4 \cos{\left(\frac{1}{4} \right)} 
4 - 4*cos(1/4)
Numerical answer [src] 
0.124350313157421
0.124350313157421
The graph
Integral of sin(x/4)dx dx

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

    © Mister Exam – Calculator