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Solving integrals/ sqrt(100-x^2)^2

Integral of sqrt(100-x^2)^2 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 38/5                 
   /                  
  |                   
  |               2   
  |     __________    
  |    /        2     
  |  \/  100 - x    dx
  |                   
 /                    
37/5
$$\int\limits_{\frac{37}{5}}^{\frac{38}{5}} \left(\sqrt{100 - x^{2}}\right)^{2}\, dx$$ 
Integral((sqrt(100 - x^2))^2, (x, 37/5, 38/5))
Detail solution

    TrigSubstitutionRule(theta=_theta, func=10*sin(_theta), rewritten=1000*cos(_theta)**3, substep=ConstantTimesRule(constant=1000, other=cos(_theta)**3, substep=RewriteRule(rewritten=(1 - sin(_theta)**2)*cos(_theta), substep=AlternativeRule(alternatives=[URule(u_var=_u, u_func=sin(_theta), constant=1, substep=AddRule(substeps=[ConstantRule(constant=1, context=1, symbol=_u), ConstantTimesRule(constant=-1, other=_u**2, substep=PowerRule(base=_u, exp=2, context=_u**2, symbol=_u), context=-_u**2, symbol=_u)], context=1 - _u**2, symbol=_u), context=(1 - sin(_theta)**2)*cos(_theta), symbol=_theta), RewriteRule(rewritten=-sin(_theta)**2*cos(_theta) + cos(_theta), substep=AddRule(substeps=[ConstantTimesRule(constant=-1, other=sin(_theta)**2*cos(_theta), substep=URule(u_var=_u, u_func=sin(_theta), constant=1, substep=PowerRule(base=_u, exp=2, context=_u**2, symbol=_u), context=sin(_theta)**2*cos(_theta), symbol=_theta), context=-sin(_theta)**2*cos(_theta), symbol=_theta), TrigRule(func='cos', arg=_theta, context=cos(_theta), symbol=_theta)], context=-sin(_theta)**2*cos(_theta) + cos(_theta), symbol=_theta), context=(1 - sin(_theta)**2)*cos(_theta), symbol=_theta), RewriteRule(rewritten=-sin(_theta)**2*cos(_theta) + cos(_theta), substep=AddRule(substeps=[ConstantTimesRule(constant=-1, other=sin(_theta)**2*cos(_theta), substep=URule(u_var=_u, u_func=sin(_theta), constant=1, substep=PowerRule(base=_u, exp=2, context=_u**2, symbol=_u), context=sin(_theta)**2*cos(_theta), symbol=_theta), context=-sin(_theta)**2*cos(_theta), symbol=_theta), TrigRule(func='cos', arg=_theta, context=cos(_theta), symbol=_theta)], context=-sin(_theta)**2*cos(_theta) + cos(_theta), symbol=_theta), context=(1 - sin(_theta)**2)*cos(_theta), symbol=_theta)], context=(1 - sin(_theta)**2)*cos(_theta), symbol=_theta), context=cos(_theta)**3, symbol=_theta), context=1000*cos(_theta)**3, symbol=_theta), restriction=(x > -10) & (x < 10), context=(sqrt(100 - x**2))**2, symbol=x)

  1. Now simplify:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                                               
 |                                                                
 |              2                                                 
 |    __________           //         3                          \
 |   /        2            ||        x                           |
 | \/  100 - x    dx = C + |<100*x - --  for And(x > -10, x < 10)|
 |                         ||        3                           |
/                          \\                                    /
$$\int \left(\sqrt{100 - x^{2}}\right)^{2}\, dx = C + \begin{cases} - \frac{x^{3}}{3} + 100 x & \text{for}\: x > -10 \wedge x < 10 \end{cases}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
3281
----
375
$$\frac{3281}{375}$$ 
=
= 
3281
----
375
$$\frac{3281}{375}$$ 
3281/375
Numerical answer [src] 
8.7493333333333
8.7493333333333

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

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