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sqrt(3-x^2)
Solving integrals/ sqrt(3-x^2)

Integral of sqrt(3-x^2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1               
  /               
 |                
 |     ________   
 |    /      2    
 |  \/  3 - x   dx
 |                
/                 
0
$$\int\limits_{0}^{1} \sqrt{3 - x^{2}}\, dx$$ 
Integral(sqrt(3 - x^2), (x, 0, 1))
Detail solution

    TrigSubstitutionRule(theta=_theta, func=sqrt(3)*sin(_theta), rewritten=3*cos(_theta)**2, substep=ConstantTimesRule(constant=3, other=cos(_theta)**2, substep=RewriteRule(rewritten=cos(2*_theta)/2 + 1/2, substep=AddRule(substeps=[ConstantTimesRule(constant=1/2, other=cos(2*_theta), substep=URule(u_var=_u, u_func=2*_theta, constant=1/2, substep=ConstantTimesRule(constant=1/2, other=cos(_u), substep=TrigRule(func='cos', arg=_u, context=cos(_u), symbol=_u), context=cos(_u), symbol=_u), context=cos(2*_theta), symbol=_theta), context=cos(2*_theta)/2, symbol=_theta), ConstantRule(constant=1/2, context=1/2, symbol=_theta)], context=cos(2*_theta)/2 + 1/2, symbol=_theta), context=cos(_theta)**2, symbol=_theta), context=3*cos(_theta)**2, symbol=_theta), restriction=(x < sqrt(3)) & (x > -sqrt(3)), context=sqrt(3 - x**2), symbol=x)

  1. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                                                                       
 |                      //      /    ___\                                                \
 |    ________          ||      |x*\/ 3 |        ________                                |
 |   /      2           ||3*asin|-------|       /      2                                 |
 | \/  3 - x   dx = C + |<      \   3   /   x*\/  3 - x           /       ___        ___\|
 |                      ||--------------- + -------------  for And\x > -\/ 3 , x < \/ 3 /|
/                       ||       2                2                                      |
                        \\                                                               /
$$\int \sqrt{3 - x^{2}}\, dx = C + \begin{cases} \frac{x \sqrt{3 - x^{2}}}{2} + \frac{3 \operatorname{asin}{\left(\frac{\sqrt{3} x}{3} \right)}}{2} & \text{for}\: x > - \sqrt{3} \wedge x < \sqrt{3} \end{cases}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
              /  ___\
              |\/ 3 |
  ___   3*asin|-----|
\/ 2          \  3  /
----- + -------------
  2           2
$$\frac{\sqrt{2}}{2} + \frac{3 \operatorname{asin}{\left(\frac{\sqrt{3}}{3} \right)}}{2}$$ 
=
= 
              /  ___\
              |\/ 3 |
  ___   3*asin|-----|
\/ 2          \  3  /
----- + -------------
  2           2
$$\frac{\sqrt{2}}{2} + \frac{3 \operatorname{asin}{\left(\frac{\sqrt{3}}{3} \right)}}{2}$$ 
sqrt(2)/2 + 3*asin(sqrt(3)/3)/2
Numerical answer [src] 
1.63032634419213
1.63032634419213
The graph
Integral of sqrt(3-x^2) dx

    Use the examples entering the upper and lower limits of integration.

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