Mister Exam
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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
- Limits Step by Step
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How to use it?
- Integral of d{x}:
- Integral of ((pi-x)/2)*cos(nx)
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Integral of kdx
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Integral of 5cosx
- Integral of (sin^4)x×(cos^4)x
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Identical expressions
- ((pi-x)/ two)*cos(nx)
- (( Pi minus x) divide by 2) multiply by co sinus of e of (nx)
- (( Pi minus x) divide by two) multiply by co sinus of e of (nx)
- ((pi-x)/2)cos(nx)
- pi-x/2cosnx
- ((pi-x) divide by 2)*cos(nx)
- ((pi-x)/2)*cos(nx)dx
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Similar expressions
- ((pi+x)/2)*cos(nx)
- (pi-x/2)*cos(n*x)
Integral of ((pi-x)/2)*cos(nx) dx
The solution
You have entered
[src]
pi / | | (pi - x)*cos(n*x) | ----------------- dx | 2 | / -pi
$$\int\limits_{- \pi}^{\pi} \frac{\left(- x + \pi\right) \cos{\left(n x \right)}}{2}\, dx$$
The answer (Indefinite)
[src]
/ 2
| x
| -- for n = 0
| 2
|
|/-cos(n*x)
<|---------- for n != 0
|< n
|| // x for n = 0\ // x for n = 0\
|\ 0 otherwise || | || |
/ |----------------------- otherwise pi*|
$$\pi\,x-{{n\,x\,\sin \left(n\,x\right)+\cos \left(n\,x\right)}\over{
2\,n^2}}$$
The answer
[src]
/pi*sin(pi*n) |------------ for And(n > -oo, n < oo, n != 0) | n < | 2 | pi otherwise \
$$2\,\pi^2$$
=
=
/pi*sin(pi*n) |------------ for And(n > -oo, n < oo, n != 0) | n < | 2 | pi otherwise \
$$\begin{cases} \frac{\pi \sin{\left(\pi n \right)}}{n} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\\pi^{2} & \text{otherwise} \end{cases}$$
Use the examples entering the upper and lower limits of integration.