Mister Exam

Other calculators

y=√1-x^2
Solving integrals/ y=√1-x^2

Integral of y=√1-x^2 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

  1. Integrate term-by-term:

    1. The integral of a constant times a function is the constant times the integral of the function:

      ∫(−x2) dx=−∫x2 dx\int \left(- x^{2}\right)\, dx = - \int x^{2}\, dx

      1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n≠−1n \neq -1:

        ∫x2 dx=x33\int x^{2}\, dx = \frac{x^{3}}{3}

      So, the result is: −x33- \frac{x^{3}}{3}

    1. The integral of a constant is the constant times the variable of integration:

      ∫1 dx=x\int \sqrt{1}\, dx = x

    The result is: −x33+x- \frac{x^{3}}{3} + x

  2. Add the constant of integration:

    −x33+x+constant- \frac{x^{3}}{3} + x+ \mathrm{constant}

The answer is:

−x33+x+constant- \frac{x^{3}}{3} + x+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                            
 |                            3
 | /  ___    2\              x 
 | \\/ 1  - x / dx = C + x - --
 |                           3 
/
∫(−x2+1) dx=C−x33+x\int \left(- x^{2} + \sqrt{1}\right)\, dx = C - \frac{x^{3}}{3} + x
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.9002
Plot the graph f(x)
The answer [src] 
2/3
23\frac{2}{3} 
=
= 
2/3
23\frac{2}{3} 
2/3
Numerical answer [src] 
0.666666666666667
0.666666666666667
The graph
Integral of y=√1-x^2 dx

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

    © Mister Exam – Calculator