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-x^2+1
Solving integrals/ -x^2+1

Integral of -x^2+1 dx

Limits of integration:

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The solution

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

  1. Integrate term-by-term:

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

      ∫1 dx=x\int 1\, dx = x

    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}

    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] 
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∫(1−x2) dx=C−x33+x\int \left(1 - x^{2}\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 -x^2+1 dx

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

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