What is the integral from x^2 to 8-x^2 of 1 ?

The integral from x^2 to 8-x^2 of 1 is 8-2x^2

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integral from x^2 to 8-x^2 of 1

\int_{x^{2}}^{8 - x^{2}} 1 d y

8 - 2 x^{2}

Solution steps

\int_{x^{2}}^{8 - x^{2}} 1 d y

Integral of a constant:

\int a d x = a x

= [1 \cdot y]_{x^{2}}^{8 - x^{2}}

Simplify

= [y]_{x^{2}}^{8 - x^{2}}

Compute the boundaries:

8 - 2 x^{2}

= 8 - 2 x^{2}

What is the integral from x^2 to 8-x^2 of 1 ?
The integral from x^2 to 8-x^2 of 1 is 8-2x^2