Mister Exam

Other calculators

Solving integrals/ (4-9x)*sin(nx)

Integral of (4-9x)*sin(nx) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 pi                      
  /                      
 |                       
 |  (4 - 9*x)*sin(n*x) dx
 |                       
/                        
0
∫0π(4−9x)sin⁡(nx) dx\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                       /
∫(4−9x)sin⁡(nx) dx=C−9x({0for n=0−cos⁡(nx)notherwise)+9({0for n=0−{sin⁡(nx)nfor n≠0xotherwisenotherwise)+4({0for n=0−cos⁡(nx)notherwise)\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)
Simplify
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            
\
{−4cos⁡(πn)n+9πcos⁡(πn)n+4n−9sin⁡(πn)n2for n>−∞∧n<∞∧n≠00otherwise\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} 
=
= 
/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            
\
{−4cos⁡(πn)n+9πcos⁡(πn)n+4n−9sin⁡(πn)n2for n>−∞∧n<∞∧n≠00otherwise\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.

    © Mister Exam – Calculator