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sqrt(64-x^2)x
Solving integrals/ sqrt(64-x^2)x

Integral of sqrt(64-x^2)x dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  4                  
  /                  
 |                   
 |     _________     
 |    /       2      
 |  \/  64 - x  *x dx
 |                   
/                    
0
$$\int\limits_{0}^{4} x \sqrt{- x^{2} + 64}\, dx$$ 
Integral(sqrt(64 - x^2)*x, (x, 0, 4))
Detail solution

  1. Rewrite the integrand:

    SqrtQuadraticDenomRule(a=64, b=0, c=-1, coeffs=[-1, 0, 64, 0], context=(-x**3 + 64*x)/sqrt(64 - x**2), symbol=x)

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                                
 |                                                 
 |    _________               _________ /        2\
 |   /       2               /       2  |  64   x |
 | \/  64 - x  *x dx = C + \/  64 - x  *|- -- + --|
 |                                      \  3    3 /
/
$$-{{\left(64-x^2\right)^{{{3}\over{2}}}}\over{3}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
512        ___
--- - 64*\/ 3 
 3
$${{512}\over{3}}-64\,\sqrt{3}$$ 
=
= 
512        ___
--- - 64*\/ 3 
 3
$$- 64 \sqrt{3} + \frac{512}{3}$$
Simplify
Numerical answer [src] 
59.8154149822585
59.8154149822585
The graph
Integral of sqrt(64-x^2)x dx

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

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