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How to use it?
- Integral of d{x}:
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Integral of x^2/sqrt(4-x^2)
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Integral of 3cosx
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Integral of e^2x
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Integral of 6/x
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Identical expressions
- y*sin((x*y)/ two)
- y multiply by sinus of ((x multiply by y) divide by 2)
- y multiply by sinus of ((x multiply by y) divide by two)
- ysin((xy)/2)
- ysinxy/2
- y*sin((x*y) divide by 2)
- y*sin((x*y)/2)dx
Integral of y*sin((x*y)/2) dx
The solution
You have entered
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2
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2
$$\int\limits_{\frac{x}{2}}^{\frac{2}{\sqrt{\pi}}} y \sin{\left(\frac{x y}{2} \right)}\, dx$$
Integral(y*sin((x*y)/2), (x, x/2, 2/sqrt(pi)))
The answer (Indefinite)
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/ // 0 for y = 0\ | || | | /x*y\ || /x*y\ | | y*sin|---| dx = C + y*|<-2*cos|---| | | \ 2 / || \ 2 / | | ||----------- otherwise| / \\ y /
$$\int y \sin{\left(\frac{x y}{2} \right)}\, dx = C + y \left(\begin{cases} 0 & \text{for}\: y = 0 \\- \frac{2 \cos{\left(\frac{x y}{2} \right)}}{y} & \text{otherwise} \end{cases}\right)$$
The answer
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/ / y \ /x*y\ |- 2*cos|------| + 2*cos|---| for And(y > -oo, y < oo, y != 0) | | ____| \ 4 / < \\/ pi / | | 0 otherwise \
$$\begin{cases} - 2 \cos{\left(\frac{y}{\sqrt{\pi}} \right)} + 2 \cos{\left(\frac{x y}{4} \right)} & \text{for}\: y > -\infty \wedge y < \infty \wedge y \neq 0 \\0 & \text{otherwise} \end{cases}$$
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/ / y \ /x*y\ |- 2*cos|------| + 2*cos|---| for And(y > -oo, y < oo, y != 0) | | ____| \ 4 / < \\/ pi / | | 0 otherwise \
$$\begin{cases} - 2 \cos{\left(\frac{y}{\sqrt{\pi}} \right)} + 2 \cos{\left(\frac{x y}{4} \right)} & \text{for}\: y > -\infty \wedge y < \infty \wedge y \neq 0 \\0 & \text{otherwise} \end{cases}$$
Piecewise((-2*cos(y/sqrt(pi)) + 2*cos(x*y/4), (y > -oo)∧(y < oo)∧(Ne(y, 0))), (0, True))
Use the examples entering the upper and lower limits of integration.