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Identical expressions
- (four -9x)*sin(nx)
- (4 minus 9x) multiply by sinus of (nx)
- (four minus 9x) multiply by sinus of (nx)
- (4-9x)sin(nx)
- 4-9xsinnx
- (4-9x)*sin(nx)dx
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Similar expressions
- (4+9x)*sin(nx)
Integral of (4-9x)*sin(nx) dx
The solution
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[src]
pi / | | (4 - 9*x)*sin(n*x) dx | / 0
$$\int\limits_{0}^{\pi} \left(4 - 9 x\right) \sin{\left(n x \right)}\, dx$$
Integral((4 - 9*x)*sin(n*x), (x, 0, pi))
The answer (Indefinite)
[src]
// 0 for n = 0\
|| |
/ // 0 for n = 0\ || //sin(n*x) \ | // 0 for n = 0\
| || | || ||-------- for n != 0| | || |
| (4 - 9*x)*sin(n*x) dx = C + 4*|<-cos(n*x) | + 9*|<-|< n | | - 9*x*|<-cos(n*x) |
| ||---------- otherwise| || || | | ||---------- otherwise|
/ \\ n / || \\ x otherwise / | \\ n /
||------------------------- otherwise|
\\ n /
$$\int \left(4 - 9 x\right) \sin{\left(n x \right)}\, dx = C - 9 x \left(\begin{cases} 0 & \text{for}\: n = 0 \\- \frac{\cos{\left(n x \right)}}{n} & \text{otherwise} \end{cases}\right) + 9 \left(\begin{cases} 0 & \text{for}\: n = 0 \\- \frac{\begin{cases} \frac{\sin{\left(n x \right)}}{n} & \text{for}\: n \neq 0 \\x & \text{otherwise} \end{cases}}{n} & \text{otherwise} \end{cases}\right) + 4 \left(\begin{cases} 0 & \text{for}\: n = 0 \\- \frac{\cos{\left(n x \right)}}{n} & \text{otherwise} \end{cases}\right)$$
The answer
[src]
/4 9*sin(pi*n) 4*cos(pi*n) 9*pi*cos(pi*n) |- - ----------- - ----------- + -------------- for And(n > -oo, n < oo, n != 0) |n 2 n n < n | | 0 otherwise \
$$\begin{cases} - \frac{4 \cos{\left(\pi n \right)}}{n} + \frac{9 \pi \cos{\left(\pi n \right)}}{n} + \frac{4}{n} - \frac{9 \sin{\left(\pi n \right)}}{n^{2}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\0 & \text{otherwise} \end{cases}$$
=
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/4 9*sin(pi*n) 4*cos(pi*n) 9*pi*cos(pi*n) |- - ----------- - ----------- + -------------- for And(n > -oo, n < oo, n != 0) |n 2 n n < n | | 0 otherwise \
$$\begin{cases} - \frac{4 \cos{\left(\pi n \right)}}{n} + \frac{9 \pi \cos{\left(\pi n \right)}}{n} + \frac{4}{n} - \frac{9 \sin{\left(\pi n \right)}}{n^{2}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\0 & \text{otherwise} \end{cases}$$
Piecewise((4/n - 9*sin(pi*n)/n^2 - 4*cos(pi*n)/n + 9*pi*cos(pi*n)/n, (n > -oo)∧(n < oo)∧(Ne(n, 0))), (0, True))
Use the examples entering the upper and lower limits of integration.