Mister Exam
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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
- Limits Step by Step
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How to use it?
- Integral of d{x}:
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Integral of (x+1)^2
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Integral of xe^(x^2)
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Integral of x^2sinx^3dx
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Integral of sin(y)
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Identical expressions
- sqrt(two -2cos(t))
- square root of (2 minus 2 co sinus of e of (t))
- square root of (two minus 2 co sinus of e of (t))
- √(2-2cos(t))
- sqrt2-2cost
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Similar expressions
- 3*sqrt(2-2*cos(t))
- sqrt(2+2cos(t))
- ((t-sint)(sqrt(2-2cost)))
Integral of sqrt(2-2cos(t)) dt
The solution
You have entered
[src]
2*pi / | | ______________ | \/ 2 - 2*cos(t) dt | / 0
$$\int\limits_{0}^{2 \pi} \sqrt{- 2 \cos{\left(t \right)} + 2}\, dt$$
Integral(sqrt(2 - 2*cos(t)), (t, 0, 2*pi))
Detail solution
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Rewrite the integrand:
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The integral of a constant times a function is the constant times the integral of the function:
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Don't know the steps in finding this integral.
But the integral is
So, the result is:
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Add the constant of integration:
The answer is:
The answer (Indefinite)
[src]
/ / | | | ______________ ___ | ____________ | \/ 2 - 2*cos(t) dt = C + \/ 2 * | \/ 1 - cos(t) dt | | / /
$$\left(-2\,\cos t-2\right)\,\sin \left({{{\rm atan2}\left(\sin t ,
\cos t\right)+\pi}\over{2}}\right)+2\,\sin t\,\cos \left({{
{\rm atan2}\left(\sin t , \cos t\right)+\pi}\over{2}}\right)$$
The answer
[src]
2*pi
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___ | ____________
\/ 2 * | \/ 1 - cos(t) dt
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/
0
$$\sqrt{2} \int\limits_{0}^{2 \pi} \sqrt{- \cos{\left(t \right)} + 1}\, dt$$
=
=
2*pi
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___ | ____________
\/ 2 * | \/ 1 - cos(t) dt
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/
0
$$\sqrt{2} \int\limits_{0}^{2 \pi} \sqrt{- \cos{\left(t \right)} + 1}\, dt$$
Use the examples entering the upper and lower limits of integration.