Mister Exam

Other calculators

Solving integrals/ sin(5x/3)dx

Integral of sin(5x/3)dx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1            
  /            
 |             
 |     /5*x\   
 |  sin|---| dx
 |     \ 3 /   
 |             
/              
0
$$\int\limits_{0}^{1} \sin{\left(\frac{5 x}{3} \right)}\, dx$$ 
Integral(sin((5*x)/3), (x, 0, 1))
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] 
  /                       /5*x\
 |                   3*cos|---|
 |    /5*x\               \ 3 /
 | sin|---| dx = C - ----------
 |    \ 3 /              5     
 |                             
/
$$\int \sin{\left(\frac{5 x}{3} \right)}\, dx = C - \frac{3 \cos{\left(\frac{5 x}{3} \right)}}{5}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
3   3*cos(5/3)
- - ----------
5       5
$$\frac{3}{5} - \frac{3 \cos{\left(\frac{5}{3} \right)}}{5}$$ 
=
= 
3   3*cos(5/3)
- - ----------
5       5
$$\frac{3}{5} - \frac{3 \cos{\left(\frac{5}{3} \right)}}{5}$$ 
3/5 - 3*cos(5/3)/5
Numerical answer [src] 
0.657434128808625
0.657434128808625

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

    © Mister Exam – Calculator