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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of sqrt(9-3x^2)
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Integral of cos(4x-5)dx
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Integral of tan^3(x)/cos^2(x)
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Integral of cos^3(4x)
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Identical expressions
- sqrt(nine -3x^ two)
- square root of (9 minus 3x squared )
- square root of (nine minus 3x to the power of two)
- √(9-3x^2)
- sqrt(9-3x2)
- sqrt9-3x2
- sqrt(9-3x²)
- sqrt(9-3x to the power of 2)
- sqrt9-3x^2
- sqrt(9-3x^2)dx
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Similar expressions
- sqrt(9+3x^2)
Integral of sqrt(9-3x^2) dx
The solution
You have entered
[src]
1 / | | __________ | / 2 | \/ 9 - 3*x dx | / 0
$$\int\limits_{0}^{1} \sqrt{- 3 x^{2} + 9}\, dx$$
Integral(sqrt(9 - 3*x^2), (x, 0, 1))
Detail solution
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Now simplify:
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Add the constant of integration:
SqrtQuadraticRule(a=9, b=0, c=-3, context=sqrt(9 - 3*x**2), symbol=x)
The answer is:
The answer (Indefinite)
[src]
/ / ___\ | __________ ___ |x*\/ 3 | | __________ / 2 3*\/ 3 *asin|-------| | / 2 x*\/ 9 - 3*x \ 3 / | \/ 9 - 3*x dx = C + --------------- + --------------------- | 2 2 /
$${{3^{{{3}\over{2}}}\,\arcsin \left({{x}\over{\sqrt{3}}}\right)
}\over{2}}+{{x\,\sqrt{9-3\,x^2}}\over{2}}$$
The graph
The answer
[src]
/ ___\
___ |\/ 3 |
___ 3*\/ 3 *asin|-----|
\/ 6 \ 3 /
----- + -------------------
2 2
$${{3^{{{3}\over{2}}}\,\arcsin \left({{1}\over{\sqrt{3}}}\right)+
\sqrt{6}}\over{2}}$$
=
=
/ ___\
___ |\/ 3 |
___ 3*\/ 3 *asin|-----|
\/ 6 \ 3 /
----- + -------------------
2 2
$$\frac{\sqrt{6}}{2} + \frac{3 \sqrt{3} \operatorname{asin}{\left(\frac{\sqrt{3}}{3} \right)}}{2}$$
The graph
Use the examples entering the upper and lower limits of integration.