Mister Exam

Other calculators

sqrt(5-x^2)
Solving integrals/ sqrt(5-x^2)

Integral of sqrt(5-x^2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1               
  /               
 |                
 |     ________   
 |    /      2    
 |  \/  5 - x   dx
 |                
/                 
0
∫01−x2+5 dx\int\limits_{0}^{1} \sqrt{- x^{2} + 5}\, dx 
Integral(sqrt(5 - x^2), (x, 0, 1))
Detail solution

    SqrtQuadraticRule(a=5, b=0, c=-1, context=sqrt(5 - x**2), symbol=x)

  1. Add the constant of integration:

    x5−x22+5asin⁡(5x5)2+constant\frac{x \sqrt{5 - x^{2}}}{2} + \frac{5 \operatorname{asin}{\left(\frac{\sqrt{5} x}{5} \right)}}{2}+ \mathrm{constant}

The answer is:

x5−x22+5asin⁡(5x5)2+constant\frac{x \sqrt{5 - x^{2}}}{2} + \frac{5 \operatorname{asin}{\left(\frac{\sqrt{5} x}{5} \right)}}{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                           /    ___\                
 |                            |x*\/ 5 |        ________
 |    ________          5*asin|-------|       /      2 
 |   /      2                 \   5   /   x*\/  5 - x  
 | \/  5 - x   dx = C + --------------- + -------------
 |                             2                2      
/
5 arcsin⁡(x5)2+x 5−x22{{5\,\arcsin \left({{x}\over{\sqrt{5}}}\right)}\over{2}}+{{x\, \sqrt{5-x^2}}\over{2}}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.900.02.5
Plot the graph f(x)
The answer [src] 
          /  ___\
          |\/ 5 |
    5*asin|-----|
          \  5  /
1 + -------------
          2
5 arcsin⁡(15)+22{{5\,\arcsin \left({{1}\over{\sqrt{5}}}\right)+2}\over{2}} 
=
= 
          /  ___\
          |\/ 5 |
    5*asin|-----|
          \  5  /
1 + -------------
          2
1+5asin⁡(55)21 + \frac{5 \operatorname{asin}{\left(\frac{\sqrt{5}}{5} \right)}}{2}
Simplify
Numerical answer [src] 
2.15911902250202
2.15911902250202
The graph
Integral of sqrt(5-x^2) dx

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

    © Mister Exam – Calculator