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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of (x-2)^3
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Integral of cosecx
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Integral of 1/√(4-x^2)
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Integral of cos(x)*exp(x)
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Identical expressions
- (pi^ two -x^ two)*sin(nx)
- ( Pi squared minus x squared ) multiply by sinus of (nx)
- ( Pi to the power of two minus x to the power of two) multiply by sinus of (nx)
- (pi2-x2)*sin(nx)
- pi2-x2*sinnx
- (pi²-x²)*sin(nx)
- (pi to the power of 2-x to the power of 2)*sin(nx)
- (pi^2-x^2)sin(nx)
- (pi2-x2)sin(nx)
- pi2-x2sinnx
- pi^2-x^2sinnx
- (pi^2-x^2)*sin(nx)dx
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Similar expressions
- (pi^2+x^2)*sin(nx)
Integral of (pi^2-x^2)*sin(nx) dx
The solution
You have entered
[src]
pi / | | / 2 2\ | \pi - x /*sin(n*x) dx | / -pi
$$\int\limits_{- \pi}^{\pi} \left(- x^{2} + \pi^{2}\right) \sin{\left(n x \right)}\, dx$$
Integral((pi^2 - x^2)*sin(n*x), (x, -pi, pi))
The answer (Indefinite)
[src]
// 0 for n = 0\
|| |
|| //cos(n*x) x*sin(n*x) \ |
/ || ||-------- + ---------- for n != 0| |
| || || 2 n | | // 0 for n = 0\ // 0 for n = 0\
| / 2 2\ || || n | | 2 || | 2 || |
| \pi - x /*sin(n*x) dx = C + 2*|<-|< | | + pi *|<-cos(n*x) | - x *|<-cos(n*x) |
| || || 2 | | ||---------- otherwise| ||---------- otherwise|
/ || || x | | \\ n / \\ n /
|| || -- otherwise | |
|| \\ 2 / |
||-------------------------------------- otherwise|
\\ n /
$${{-{{2\,n\,x\,\sin \left(n\,x\right)+\left(2-n^2\,x^2\right)\,\cos
\left(n\,x\right)}\over{n^2}}-\pi^2\,\cos \left(n\,x\right)}\over{n
}}$$
Use the examples entering the upper and lower limits of integration.