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(1+e^(2*x))
- Integral of (x³+2x)
-
Integral of 1/3*t^3*dt
- Integral of cos(x)*cos(kx)
-
Identical expressions
- cos(x)*cos(kx)
- co sinus of e of (x) multiply by co sinus of e of (kx)
- cos(x)cos(kx)
- cosxcoskx
- cos(x)*cos(kx)dx
-
Similar expressions
- cosx*cos(kx)
Integral of cos(x)*cos(kx) dx
The solution
You have entered
[src]
pi / | | cos(x)*cos(k*x) dx | / 0
$$\int\limits_{0}^{\pi} \cos{\left(x \right)} \cos{\left(k x \right)}\, dx$$
Integral(cos(x)*cos(k*x), (x, 0, pi))
The answer (Indefinite)
[src]
// 2 2 \
||x*cos (x) x*sin (x) cos(x)*sin(x) |
/ ||--------- + --------- + ------------- for Or(k = -1, k = 1)|
| || 2 2 2 |
| cos(x)*cos(k*x) dx = C + |< |
| || cos(k*x)*sin(x) k*cos(x)*sin(k*x) |
/ ||- --------------- + ----------------- otherwise |
|| 2 2 |
\\ -1 + k -1 + k /
$${{\sin \left(\left(k+1\right)\,x\right)}\over{2\,\left(k+1\right)}}
+{{\sin \left(\left(1-k\right)\,x\right)}\over{2\,\left(1-k\right)}}$$
The answer
[src]
/ pi | -- for Or(k = -1, k = 1) | 2 | <-k*sin(pi*k) |------------- otherwise | 2 | -1 + k \
$$\begin{cases} \frac{\pi}{2} & \text{for}\: k = -1 \vee k = 1 \\- \frac{k \sin{\left(\pi k \right)}}{k^{2} - 1} & \text{otherwise} \end{cases}$$
=
=
/ pi | -- for Or(k = -1, k = 1) | 2 | <-k*sin(pi*k) |------------- otherwise | 2 | -1 + k \
$$\begin{cases} \frac{\pi}{2} & \text{for}\: k = -1 \vee k = 1 \\- \frac{k \sin{\left(\pi k \right)}}{k^{2} - 1} & \text{otherwise} \end{cases}$$
Use the examples entering the upper and lower limits of integration.