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