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Solving integrals/ 2-x^2

Integral of 2-x^2 dx

Limits of integration:

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The solution

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∫21(2−x2) dx\int\limits_{2}^{1} \left(2 - x^{2}\right)\, dx 
Integral(2 - x^2, (x, 2, 1))
Detail solution

  1. Integrate term-by-term:

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

      ∫2 dx=2x\int 2\, dx = 2 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+2x- \frac{x^{3}}{3} + 2 x

  2. Now simplify:

    x(6−x2)3\frac{x \left(6 - x^{2}\right)}{3}

  3. Add the constant of integration:

    x(6−x2)3+constant\frac{x \left(6 - x^{2}\right)}{3}+ \mathrm{constant}

The answer is:

x(6−x2)3+constant\frac{x \left(6 - x^{2}\right)}{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
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∫(2−x2) dx=C−x33+2x\int \left(2 - x^{2}\right)\, dx = C - \frac{x^{3}}{3} + 2 x
Simplify
The graph
1.002.001.101.201.301.401.501.601.701.801.905-5
Plot the graph f(x)
The answer [src] 
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13\frac{1}{3} 
=
= 
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13\frac{1}{3} 
1/3

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

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