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How to use it?
- Integral of d{x}:
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Integral of e^(-x)*sin(2*x)
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Integral of xsinx^2
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Integral of xsin(2x)dx
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Integral of 1/100
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Identical expressions
- sin(mx)*cos(nx)
- sinus of (mx) multiply by co sinus of e of (nx)
- sin(mx)cos(nx)
- sinmxcosnx
- sin(mx)*cos(nx)dx
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Similar expressions
- sin^(m)(x)*cos^(n)(x)
Integral of sin(mx)*cos(nx) dx
The solution
You have entered
[src]
pi / | | sin(m*x)*cos(n*x) dx | / -pi
$$\int\limits_{- \pi}^{\pi} \sin{\left(m x \right)} \cos{\left(n x \right)}\, dx$$
Integral(sin(m*x)*cos(n*x), (x, -pi, pi))
The answer (Indefinite)
[src]
// 0 for And(m = 0, n = 0)\
|| |
|| 2 |
|| -sin (n*x) |
|| ----------- for m = -n |
|| 2*n |
/ || |
| || 2 |
| sin(m*x)*cos(n*x) dx = C + |< sin (n*x) |
| || --------- for m = n |
/ || 2*n |
|| |
|| m*cos(m*x)*cos(n*x) n*sin(m*x)*sin(n*x) |
||- ------------------- - ------------------- otherwise |
|| 2 2 2 2 |
|| m - n m - n |
\\ /
$$\int \sin{\left(m x \right)} \cos{\left(n x \right)}\, dx = C + \begin{cases} 0 & \text{for}\: m = 0 \wedge n = 0 \\- \frac{\sin^{2}{\left(n x \right)}}{2 n} & \text{for}\: m = - n \\\frac{\sin^{2}{\left(n x \right)}}{2 n} & \text{for}\: m = n \\- \frac{m \cos{\left(m x \right)} \cos{\left(n x \right)}}{m^{2} - n^{2}} - \frac{n \sin{\left(m x \right)} \sin{\left(n x \right)}}{m^{2} - n^{2}} & \text{otherwise} \end{cases}$$
Use the examples entering the upper and lower limits of integration.