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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 sqrt(8-2x-x^2)
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Integral of 6t^2-4t
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Integral of sinh^2(x)
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Integral of cos⁵xdx
- Graphing y =:
- sqrt(8-2x-x^2)
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Identical expressions
- sqrt(eight - two x-x^2)
- square root of (8 minus 2x minus x squared )
- square root of (eight minus two x minus x squared )
- √(8-2x-x^2)
- sqrt(8-2x-x2)
- sqrt8-2x-x2
- sqrt(8-2x-x²)
- sqrt(8-2x-x to the power of 2)
- sqrt8-2x-x^2
- sqrt(8-2x-x^2)dx
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Similar expressions
- sqrt(8+2x-x^2)
- sqrt(8-2x+x^2)
Integral of sqrt(8-2x-x^2) dx
The solution
You have entered
[src]
1 / | | ______________ | / 2 | \/ 8 - 2*x - x dx | / 0
$$\int\limits_{0}^{1} \sqrt{- x^{2} - 2 x + 8}\, dx$$
Integral(sqrt(8 - 2*x - x^2), (x, 0, 1))
Detail solution
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Now simplify:
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Add the constant of integration:
SqrtQuadraticRule(a=8, b=-2, c=-1, context=sqrt(-x**2 - 2*x + 8), symbol=x)
The answer is:
The answer (Indefinite)
[src]
/ | /1 x\ | ______________ 9*asin|- + -| ______________ | / 2 \3 3/ / 2 /1 x\ | \/ 8 - 2*x - x dx = C + ------------- + \/ 8 - x - 2*x *|- + -| | 2 \2 2/ /
$${{x\,\sqrt{-x^2-2\,x+8}}\over{2}}+{{\sqrt{-x^2-2\,x+8}}\over{2}}-{{
9\,\arcsin \left({{-2\,x-2}\over{6}}\right)}\over{2}}$$
The graph
The answer
[src]
___ ___ 9*asin(1/3) 9*asin(2/3)
\/ 5 - \/ 2 - ----------- + -----------
2 2
$${{9\,\arcsin \left({{2}\over{3}}\right)+2\,\sqrt{5}}\over{2}}-{{9\,
\arcsin \left({{1}\over{3}}\right)+2^{{{3}\over{2}}}}\over{2}}$$
=
=
___ ___ 9*asin(1/3) 9*asin(2/3)
\/ 5 - \/ 2 - ----------- + -----------
2 2
$$- \frac{9 \operatorname{asin}{\left(\frac{1}{3} \right)}}{2} - \sqrt{2} + \sqrt{5} + \frac{9 \operatorname{asin}{\left(\frac{2}{3} \right)}}{2}$$
The graph
Use the examples entering the upper and lower limits of integration.