Help Notes: `int_-5^5(x - sqrt(25 - x^2))dx` Evaluate the integral by interpreting it in terms of areas.

Wednesday, 11 May 2011

$\displaystyle{\int_{{-{{5}}}}^{{5}}}{\left({x}-\sqrt{{{25}-{{x}}^{{2}}}}\right)}{\left.{d}{x}\right.}$ Evaluate the integral by interpreting it in terms of areas.

gsarora17

$\displaystyle{\int_{{-{{5}}}}^{{5}}}{\left({x}-\sqrt{{{25}-{{x}}^{{2}}}}\right)}{\left.{d}{x}\right.}$

$\displaystyle={\int_{{-{{5}}}}^{{5}}}{x}{\left.{d}{x}\right.}-{\int_{{-{{5}}}}^{{5}}}\sqrt{{{25}-{{x}}^{{2}}}}{\left.{d}{x}\right.}$

$\displaystyle={I}_{{1}}-{I}_{{2}}$

I_1 can be be interpreted as area of two triangles;one above the x-axis and the other
below axis.Since they are on...

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Help Notes

Wednesday, 11 May 2011

$\displaystyle{\int_{{-{{5}}}}^{{5}}}{\left({x}-\sqrt{{{25}-{{x}}^{{2}}}}\right)}{\left.{d}{x}\right.}$ Evaluate the integral by interpreting it in terms of areas.

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