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sqrt(1-4y^2)
Solving integrals/ sqrt(1-4y^2)

Integral of sqrt(1-4y^2) dx

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

You have entered [src] 
  0                 
  /                 
 |                  
 |     __________   
 |    /        2    
 |  \/  1 - 4*y   dy
 |                  
/                   
-3
∫−30−4y2+1 dy\int\limits_{-3}^{0} \sqrt{- 4 y^{2} + 1}\, dy 
Integral(sqrt(1 - 4*y^2), (y, -3, 0))
Detail solution

    SqrtQuadraticRule(a=1, b=0, c=-4, context=sqrt(1 - 4*y**2), symbol=y)

  1. Add the constant of integration:

    y1−4y22+asin⁡(2y)4+constant\frac{y \sqrt{1 - 4 y^{2}}}{2} + \frac{\operatorname{asin}{\left(2 y \right)}}{4}+ \mathrm{constant}

The answer is:

y1−4y22+asin⁡(2y)4+constant\frac{y \sqrt{1 - 4 y^{2}}}{2} + \frac{\operatorname{asin}{\left(2 y \right)}}{4}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                                  
 |                                         __________
 |    __________                          /        2 
 |   /        2           asin(2*y)   y*\/  1 - 4*y  
 | \/  1 - 4*y   dy = C + --------- + ---------------
 |                            4              2       
/
arcsin⁡(2 y)4+y 1−4 y22{{\arcsin \left(2\,y\right)}\over{4}}+{{y\,\sqrt{1-4\,y^2}}\over{2 }}
Simplify
The graph
-3.00-2.75-2.50-2.25-2.00-1.75-1.50-1.25-1.00-0.75-0.50-0.250.002-2
Plot the graph f(x)
The answer [src] 
                ____
asin(6)   3*I*\/ 35 
------- + ----------
   4          2
asin⁡(6)4+335i2\frac{\operatorname{asin}{\left(6 \right)}}{4} + \frac{3 \sqrt{35} i}{2} 
=
= 
                ____
asin(6)   3*I*\/ 35 
------- + ----------
   4          2
asin⁡(6)4+335i2\frac{\operatorname{asin}{\left(6 \right)}}{4} + \frac{3 \sqrt{35} i}{2}
Simplify
Numerical answer [src] 
(0.393117529066759 + 8.25507745523633j)
(0.393117529066759 + 8.25507745523633j)
The graph
Integral of sqrt(1-4y^2) dx

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

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