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

Integral of dx/sqrt(3-x^2) dx

The solution

You have entered [src]

  1               
  /               
 |                
 |       1        
 |  ----------- dx
 |     ________   
 |    /      2    
 |  \/  3 - x     
 |                
/                 
0

$$\int\limits_{0}^{1} \frac{1}{\sqrt{3 - x^{2}}}\, dx$$

Integral(1/(sqrt(3 - x^2)), (x, 0, 1))

Detail solution

TrigSubstitutionRule(theta=_theta, func=sqrt(3)*sin(_theta), rewritten=1, substep=ConstantRule(constant=1, context=1, symbol=_theta), restriction=(x < sqrt(3)) & (x > -sqrt(3)), context=1/(sqrt(3 - x**2)), symbol=x)

Add the constant of integration:

$\begin{cases} \operatorname{asin}{\left(\frac{\sqrt{3} x}{3} \right)} & \text{for}\: x > - \sqrt{3} \wedge x < \sqrt{3} \end{cases}+ \mathrm{constant}$

The answer is:

$\begin{cases} \operatorname{asin}{\left(\frac{\sqrt{3} x}{3} \right)} & \text{for}\: x > - \sqrt{3} \wedge x < \sqrt{3} \end{cases}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                                     
 |                      //    /    ___\                                \
 |      1               ||    |x*\/ 3 |         /       ___        ___\|
 | ----------- dx = C + | -\/ 3 , x < \/ 3 /|
 |    ________          ||    \   3   /                                |
 |   /      2           \\                                             /
 | \/  3 - x                                                            
 |                                                                      
/

$$\int \frac{1}{\sqrt{3 - x^{2}}}\, dx = C + \begin{cases} \operatorname{asin}{\left(\frac{\sqrt{3} x}{3} \right)} & \text{for}\: x > - \sqrt{3} \wedge x < \sqrt{3} \end{cases}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

    /  ___\
    |\/ 3 |
asin|-----|
    \  3  /

$$\operatorname{asin}{\left(\frac{\sqrt{3}}{3} \right)}$$

    /  ___\
    |\/ 3 |
asin|-----|
    \  3  /

$$\operatorname{asin}{\left(\frac{\sqrt{3}}{3} \right)}$$

asin(sqrt(3)/3)

Numerical answer [src]

0.615479708670387

0.615479708670387

The graph

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

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Identical expressions

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Integral of dx/sqrt(3-x^2) dx

Limits of integration:

The graph:

Piecewise:

The solution