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- Improper integral
- Double Integral
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How to use it?
- Integral of d{x}:
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Integral of e^(3*x)
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Integral of y^(-2)
- Integral of 1/y
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Integral of secx
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Identical expressions
- (- one -x)cos((npix)/ two)
- ( minus 1 minus x) co sinus of e of ((n Pi x) divide by 2)
- ( minus one minus x) co sinus of e of ((n Pi x) divide by two)
- -1-xcosnpix/2
- (-1-x)cos((npix) divide by 2)
- (-1-x)cos((npix)/2)dx
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Similar expressions
- (1-x)cos((npix)/2)
- (-1+x)cos((npix)/2)
Integral of (-1-x)cos((npix)/2) dx
The solution
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[src]
2 / | | /n*pi*x\ | (-1 - x)*cos|------| dx | \ 2 / | / -2
$$\int\limits_{-2}^{2} \left(- x - 1\right) \cos{\left(\frac{\pi n x}{2} \right)}\, dx$$
Integral((-1 - x)*cos(n*pi*x/2), (x, -2, 2))
The answer (Indefinite)
[src]
// 2 \
|| x |
|| -- for n = 0|
|| 2 |
/ // x for n = 0\ // x for n = 0\ || |
| || | || | || // /pi*n*x\ \ |
| /n*pi*x\ || /pi*n*x\ | || /pi*n*x\ | || ||-2*cos|------| | |
| (-1 - x)*cos|------| dx = C - |<2*sin|------| | - x*|<2*sin|------| | + |< || \ 2 / | |
| \ 2 / || \ 2 / | || \ 2 / | ||2*|<-------------- for pi*n != 0| |
| ||------------- otherwise| ||------------- otherwise| || || pi*n | |
/ \\ pi*n / \\ pi*n / || || | |
|| \\ 0 otherwise / |
||---------------------------------- otherwise|
|| pi*n |
\\ /
$$\int \left(- x - 1\right) \cos{\left(\frac{\pi n x}{2} \right)}\, dx = C - x \left(\begin{cases} x & \text{for}\: n = 0 \\\frac{2 \sin{\left(\frac{\pi n x}{2} \right)}}{\pi n} & \text{otherwise} \end{cases}\right) - \begin{cases} x & \text{for}\: n = 0 \\\frac{2 \sin{\left(\frac{\pi n x}{2} \right)}}{\pi n} & \text{otherwise} \end{cases} + \begin{cases} \frac{x^{2}}{2} & \text{for}\: n = 0 \\\frac{2 \left(\begin{cases} - \frac{2 \cos{\left(\frac{\pi n x}{2} \right)}}{\pi n} & \text{for}\: \pi n \neq 0 \\0 & \text{otherwise} \end{cases}\right)}{\pi n} & \text{otherwise} \end{cases}$$
The answer
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/-4*sin(pi*n) |------------ for And(n > -oo, n < oo, n != 0) < pi*n | \ -4 otherwise
$$\begin{cases} - \frac{4 \sin{\left(\pi n \right)}}{\pi n} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\-4 & \text{otherwise} \end{cases}$$
=
=
/-4*sin(pi*n) |------------ for And(n > -oo, n < oo, n != 0) < pi*n | \ -4 otherwise
$$\begin{cases} - \frac{4 \sin{\left(\pi n \right)}}{\pi n} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\-4 & \text{otherwise} \end{cases}$$
Use the examples entering the upper and lower limits of integration.