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Integral of (4-x^2)^0.5
Identical expressions
(four -x^ two)^ zero . five
(4 minus x squared ) to the power of 0.5
(four minus x to the power of two) to the power of zero . five
(4-x2)0.5
4-x20.5
(4-x²)^0.5
(4-x to the power of 2) to the power of 0.5
4-x^2^0.5
(4-x^2)^0.5dx
Similar expressions
(4+x^2)^0.5

Solving integrals/ (4-x^2)^0.5

Integral of (4-x^2)^0.5 dx

The solution

You have entered [src]

  1               
  /               
 |                
 |     ________   
 |    /      2    
 |  \/  4 - x   dx
 |                
/                 
0

$$\int\limits_{0}^{1} \sqrt{4 - x^{2}}\, dx$$

Integral(sqrt(4 - x^2), (x, 0, 1))

Detail solution

TrigSubstitutionRule(theta=_theta, func=2*sin(_theta), rewritten=4*cos(_theta)**2, substep=ConstantTimesRule(constant=4, 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=4*cos(_theta)**2, symbol=_theta), restriction=(x > -2) & (x < 2), context=sqrt(4 - x**2), symbol=x)

Add the constant of integration:

$\begin{cases} \frac{x \sqrt{4 - x^{2}}}{2} + 2 \operatorname{asin}{\left(\frac{x}{2} \right)} & \text{for}\: x > -2 \wedge x < 2 \end{cases}+ \mathrm{constant}$

The answer is:

$\begin{cases} \frac{x \sqrt{4 - x^{2}}}{2} + 2 \operatorname{asin}{\left(\frac{x}{2} \right)} & \text{for}\: x > -2 \wedge x < 2 \end{cases}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                                         
 |                                                                          
 |    ________          //                 ________                        \
 |   /      2           ||                /      2                         |
 | \/  4 - x   dx = C + |<      /x\   x*\/  4 - x                          |
 |                      ||2*asin|-| + -------------  for And(x > -2, x < 2)|
/                       \\      \2/         2                              /

$$\int \sqrt{4 - x^{2}}\, dx = C + \begin{cases} \frac{x \sqrt{4 - x^{2}}}{2} + 2 \operatorname{asin}{\left(\frac{x}{2} \right)} & \text{for}\: x > -2 \wedge x < 2 \end{cases}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

  ___     
\/ 3    pi
----- + --
  2     3

$$\frac{\sqrt{3}}{2} + \frac{\pi}{3}$$

  ___     
\/ 3    pi
----- + --
  2     3

$$\frac{\sqrt{3}}{2} + \frac{\pi}{3}$$

sqrt(3)/2 + pi/3

Numerical answer [src]

1.91322295498104

1.91322295498104

The graph

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

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Integral of (4-x^2)^0.5 dx

Limits of integration:

The graph:

Piecewise:

The solution