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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 x/(x^3+8)
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Integral of x^(-6)
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Integral of -x^-2
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Integral of 1/(1+sqrt(x+1))
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Identical expressions
- sqrt((two . five (one -cosx))^ two +(two .5sinx)^ two)
- square root of ((2.5(1 minus co sinus of e of x)) squared plus (2.5 sinus of x) squared )
- square root of ((two . five (one minus co sinus of e of x)) to the power of two plus (two .5 sinus of x) to the power of two)
- √((2.5(1-cosx))^2+(2.5sinx)^2)
- sqrt((2.5(1-cosx))2+(2.5sinx)2)
- sqrt2.51-cosx2+2.5sinx2
- sqrt((2.5(1-cosx))²+(2.5sinx)²)
- sqrt((2.5(1-cosx)) to the power of 2+(2.5sinx) to the power of 2)
- sqrt2.51-cosx^2+2.5sinx^2
- sqrt((2.5(1-cosx))^2+(2.5sinx)^2)dx
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Similar expressions
- sqrt((2.5(1+cosx))^2+(2.5sinx)^2)
- sqrt((2.5(1-cosx))^2-(2.5sinx)^2)
Integral of sqrt((2.5(1-cosx))^2+(2.5sinx)^2) dx
The solution
You have entered
[src]
1 / | | _________________________________ | / 2 2 | / /5*(1 - cos(x))\ /5*sin(x)\ | / |--------------| + |--------| dx | \/ \ 2 / \ 2 / | / 0
$$\int\limits_{0}^{1} \sqrt{\left(\frac{5 \left(1 - \cos{\left(x \right)}\right)}{2}\right)^{2} + \left(\frac{5 \sin{\left(x \right)}}{2}\right)^{2}}\, dx$$
Integral(sqrt((5*(1 - cos(x))/2)^2 + (5*sin(x)/2)^2), (x, 0, 1))
The answer (Indefinite)
[src]
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/ | __________________________________
| | / 2 2
| _________________________________ 5* | \/ 1 + cos (x) + sin (x) - 2*cos(x) dx
| / 2 2 |
| / /5*(1 - cos(x))\ /5*sin(x)\ /
| / |--------------| + |--------| dx = C + ---------------------------------------------
| \/ \ 2 / \ 2 / 2
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$$\int \sqrt{\left(\frac{5 \left(1 - \cos{\left(x \right)}\right)}{2}\right)^{2} + \left(\frac{5 \sin{\left(x \right)}}{2}\right)^{2}}\, dx = C + \frac{5 \int \sqrt{\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)} - 2 \cos{\left(x \right)} + 1}\, dx}{2}$$
The answer
[src]
1
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| __________________________________
| / 2 2
5* | \/ 1 + cos (x) + sin (x) - 2*cos(x) dx
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/
0
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2
$$\frac{5 \int\limits_{0}^{1} \sqrt{\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)} - 2 \cos{\left(x \right)} + 1}\, dx}{2}$$
=
=
1
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| __________________________________
| / 2 2
5* | \/ 1 + cos (x) + sin (x) - 2*cos(x) dx
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0
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2
$$\frac{5 \int\limits_{0}^{1} \sqrt{\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)} - 2 \cos{\left(x \right)} + 1}\, dx}{2}$$
5*Integral(sqrt(1 + cos(x)^2 + sin(x)^2 - 2*cos(x)), (x, 0, 1))/2
Use the examples entering the upper and lower limits of integration.