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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of 1/(2+x^2)
- Integral of sin(w*t)^2
- Integral of sin(log(x))^2/x
- Integral of sin^n(x)
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Identical expressions
- sin(w*t)^ two
- sinus of (w multiply by t) squared
- sinus of (w multiply by t) to the power of two
- sin(w*t)2
- sinw*t2
- sin(w*t)²
- sin(w*t) to the power of 2
- sin(wt)^2
- sin(wt)2
- sinwt2
- sinwt^2
Integral of sin(w*t)^2 dx
The solution
You have entered
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1 / | | 2 | sin (w*t) dw | / 0
$$\int\limits_{0}^{1} \sin^{2}{\left(t w \right)}\, dw$$
Integral(sin(w*t)^2, (w, 0, 1))
The answer (Indefinite)
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/ w for t = 0
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/
$$\int \sin^{2}{\left(t w \right)}\, dw = C + \frac{w}{2} - \frac{\begin{cases} w & \text{for}\: t = 0 \\\frac{\sin{\left(2 t w \right)}}{2 t} & \text{otherwise} \end{cases}}{2}$$
The answer
[src]
/t cos(t)*sin(t) |- - ------------- |2 2 <----------------- for And(t > -oo, t < oo, t != 0) | t | \ 0 otherwise
$$\begin{cases} \frac{\frac{t}{2} - \frac{\sin{\left(t \right)} \cos{\left(t \right)}}{2}}{t} & \text{for}\: t > -\infty \wedge t < \infty \wedge t \neq 0 \\0 & \text{otherwise} \end{cases}$$
=
=
/t cos(t)*sin(t) |- - ------------- |2 2 <----------------- for And(t > -oo, t < oo, t != 0) | t | \ 0 otherwise
$$\begin{cases} \frac{\frac{t}{2} - \frac{\sin{\left(t \right)} \cos{\left(t \right)}}{2}}{t} & \text{for}\: t > -\infty \wedge t < \infty \wedge t \neq 0 \\0 & \text{otherwise} \end{cases}$$
Piecewise(((t/2 - cos(t)*sin(t)/2)/t, (t > -oo)∧(t < oo)∧(Ne(t, 0))), (0, True))
Use the examples entering the upper and lower limits of integration.