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Integral of d{x}:
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Identical expressions
√(one -(4x⁴- one /4x²))
√(1 minus (4x⁴ minus 1 divide by 4x²))
√(one minus (4x⁴ minus one divide by 4x²))
√1-4x⁴-1/4x²
√(1-(4x⁴-1 divide by 4x²))
√(1-(4x⁴-1/4x²))dx
Similar expressions
√(1-(4x⁴+1/4x²))
√(1+(4x⁴-1/4x²))

Integral of √(1-(4x⁴-1/4x²)) dx

The solution

You have entered [src]

  2                          
  /                          
 |                           
 |       _________________   
 |      /     /        2\    
 |     /      |   4   x |    
 |    /   1 - |4*x  - --|  dx
 |  \/        \       4 /    
 |                           
/                            
1

$$\int\limits_{1}^{2} \sqrt{- (4 x^{4} - \frac{x^{2}}{4}) + 1}\, dx$$

Integral(sqrt(1 - (4*x^4 - x^2/4)), (x, 1, 2))

Detail solution

Rewrite the integrand:

$\text{True}$
The integral of a constant times a function is the constant times the integral of the function:

$\int \frac{\sqrt{- 16 x^{4} + x^{2} + 4}}{2}\, dx = \frac{\int \sqrt{- 16 x^{4} + x^{2} + 4}\, dx}{2}$
1. Don't know the steps in finding this integral.
  
  But the integral is
  
  $\int \sqrt{- 16 x^{4} + x^{2} + 4}\, dx$
So, the result is: $\frac{\int \sqrt{- 16 x^{4} + x^{2} + 4}\, dx}{2}$
Add the constant of integration:

$\frac{\int \sqrt{- 16 x^{4} + x^{2} + 4}\, dx}{2}+ \mathrm{constant}$

The answer is:

$\frac{\int \sqrt{- 16 x^{4} + x^{2} + 4}\, dx}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

                                     /                      
                                    |                       
  /                                 |    ________________   
 |                                  |   /      2       4    
 |      _________________           | \/  4 + x  - 16*x   dx
 |     /     /        2\            |                       
 |    /      |   4   x |           /                        
 |   /   1 - |4*x  - --|  dx = C + -------------------------
 | \/        \       4 /                       2            
 |                                                          
/

$$\int {\sqrt{-4\,x^4+{{x^2}\over{4}}+1}}{\;dx}$$

The answer [src]

  2                       
  /                       
 |                        
 |     ________________   
 |    /      2       4    
 |  \/  4 + x  - 16*x   dx
 |                        
/                         
1                         
--------------------------
            2

$$\int_{1}^{2}{\sqrt{-4\,x^4+{{x^2}\over{4}}+1}\;dx}$$

  2                       
  /                       
 |                        
 |     ________________   
 |    /      2       4    
 |  \/  4 + x  - 16*x   dx
 |                        
/                         
1                         
--------------------------
            2

$$\frac{\int\limits_{1}^{2} \sqrt{- 16 x^{4} + x^{2} + 4}\, dx}{2}$$

Simplify

Numerical answer [src]

(0.0 + 4.47278782879236j)

(0.0 + 4.47278782879236j)

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

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Identical expressions

Similar expressions

Integral of √(1-(4x⁴-1/4x²)) dx

Limits of integration:

The graph:

Piecewise:

The solution