Mister Exam
Other calculators
- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
- Limits Step by Step
-
How to use it?
- Integral of d{x}:
-
Integral of sqrt(x)*e^(-x)
- Integral of sin(mx)cos(nx)
- Integral of sqrt(1+4t^2+4t^4)
-
Integral of sinh^4x
-
Identical expressions
- sin(mx)cos(nx)
- sinus of (mx) co sinus of e of (nx)
- sinmxcosnx
- sin(mx)cos(nx)dx
-
Similar expressions
- sin(mx)*cos(nx)
- 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
$$\int\limits_{- \pi}^{\pi} \sin{\left(m x \right)} \cos{\left(n x \right)}\, dx$$
The answer (Indefinite)
[src]
// 0 for And(m = 0, n = 0)\
|| |
|| 2 |
|| cos (n*x) |
|| --------- for m = -n |
|| 2*n |
/ || |
| || 2 |
| sin(m*x)*cos(n*x) dx = C + |< -cos (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 |
\\ /
$$-{{\cos \left(\left(n+m\right)\,x\right)}\over{2\,\left(n+m\right)
}}-{{\cos \left(\left(m-n\right)\,x\right)}\over{2\,\left(m-n\right)
}}$$
Use the examples entering the upper and lower limits of integration.