Mister Exam

Other calculators

sin(5x)*sin(3x)
Solving integrals/ sin(5x)*sin(3x)

Integral of sin(5x)*sin(3x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                     
  /                     
 |                      
 |  sin(5*x)*sin(3*x) dx
 |                      
/                       
0
$$\int\limits_{0}^{1} \sin{\left(3 x \right)} \sin{\left(5 x \right)}\, dx$$ 
Integral(sin(5*x)*sin(3*x), (x, 0, 1))
The graph
Plot the graph f(x)
The answer [src] 
  5*cos(5)*sin(3)   3*cos(3)*sin(5)
- --------------- + ---------------
         16                16
$$- \frac{5 \sin{\left(3 \right)} \cos{\left(5 \right)}}{16} + \frac{3 \sin{\left(5 \right)} \cos{\left(3 \right)}}{16}$$ 
=
= 
  5*cos(5)*sin(3)   3*cos(3)*sin(5)
- --------------- + ---------------
         16                16
$$- \frac{5 \sin{\left(3 \right)} \cos{\left(5 \right)}}{16} + \frac{3 \sin{\left(5 \right)} \cos{\left(3 \right)}}{16}$$ 
-5*cos(5)*sin(3)/16 + 3*cos(3)*sin(5)/16
Numerical answer [src] 
0.165489466292459
0.165489466292459
The graph
Integral of sin(5x)*sin(3x) dx

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

    © Mister Exam – Calculator