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sin(5x)*sin(3x)

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

Limits of integration:

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The graph:

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Piecewise:

The solution

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$$\int\limits_{0}^{1} \sin{\left(3 x \right)} \sin{\left(5 x \right)}\, dx$$
Integral(sin(5*x)*sin(3*x), (x, 0, 1))
The graph
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.