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sqrt(10-x^2)
Solving integrals/ sqrt(10-x^2)

Integral of sqrt(10-x^2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                
  /                
 |                 
 |     _________   
 |    /       2    
 |  \/  10 - x   dx
 |                 
/                  
0
∫01−x2+10 dx\int\limits_{0}^{1} \sqrt{- x^{2} + 10}\, dx
Simplify
Detail solution

    SqrtQuadraticRule(a=10, b=0, c=-1, context=sqrt(10 - x**2), symbol=x)

  1. Add the constant of integration:

    x10−x22+5asin⁡(10x10)+constant\frac{x \sqrt{10 - x^{2}}}{2} + 5 \operatorname{asin}{\left(\frac{\sqrt{10} x}{10} \right)}+ \mathrm{constant}

The answer is:

x10−x22+5asin⁡(10x10)+constant\frac{x \sqrt{10 - x^{2}}}{2} + 5 \operatorname{asin}{\left(\frac{\sqrt{10} x}{10} \right)}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                                       
 |                                               _________
 |    _________                /    ____\       /       2 
 |   /       2                 |x*\/ 10 |   x*\/  10 - x  
 | \/  10 - x   dx = C + 5*asin|--------| + --------------
 |                             \   10   /         2       
/
5 arcsin⁡(x10)+x 10−x225\,\arcsin \left({{x}\over{\sqrt{10}}}\right)+{{x\,\sqrt{10-x^2} }\over{2}}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.9005
Plot the graph f(x)
The answer [src] 
          /  ____\
3         |\/ 10 |
- + 5*asin|------|
2         \  10  /
10 arcsin⁡(110)+32{{10\,\arcsin \left({{1}\over{\sqrt{10}}}\right)+3}\over{2}} 
=
= 
          /  ____\
3         |\/ 10 |
- + 5*asin|------|
2         \  10  /
32+5asin⁡(1010)\frac{3}{2} + 5 \operatorname{asin}{\left(\frac{\sqrt{10}}{10} \right)}
Simplify
Numerical answer [src] 
3.10875277198321
3.10875277198321
The graph
Integral of sqrt(10-x^2) dx

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

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