Notes: `y = 12 - x^2, y = x^2 - 6` Sketch the region enclosed by the given curves and find its area.

Sunday, 1 February 2015

$\displaystyle{y}={12}-{{x}}^{{2}},{y}={{x}}^{{2}}-{6}$ Sketch the region enclosed by the given curves and find its area.

$\displaystyle{y}={12}-{{x}}^{{2}},{y}={{x}}^{{2}}-{6}$

Refer the attached image. Graph of y=12-x^2 is plotted in blue color and graph of y=x^2-6 is plotted in red color. The curves intersects at x= $\displaystyle\pm$ 3

Area of the region enclosed by the given curves A= $\displaystyle{\int_{{-{3}}}^{{3}}}{\left({\left({12}-{{x}}^{{2}}\right)}-{\left({{x}}^{{2}}-{6}\right)}\right)}{\left.{d}{x}\right.}$

$\displaystyle{A}={\int_{{-{3}}}^{{3}}}{\left({12}-{{x}}^{{2}}-{{x}}^{{2}}+{6}\right)}{\left.{d}{x}\right.}$

$\displaystyle{A}={2}{\int_{{0}}^{{3}}}{\left({18}-{2}{{x}}^{{2}}\right)}{\left.{d}{x}\right.}$

$\displaystyle{A}={2}{{\left[{18}{x}-{2}\frac{{{x}}^{{3}}}{{3}}\right]}_{{0}}^{{3}}}$

$\displaystyle{A}={2}{\left({18}\cdot{3}-\frac{{2}}{{3}}{\left({{3}}^{{3}}\right)}\right)}$

$\displaystyle{A}={2}{\left({54}-\frac{{54}}{{3}}\right)}$

$\displaystyle{A}={2}{\left(\frac{{108}}{{3}}\right)}$

$\displaystyle{A}={72}$

$\displaystyle{y}={12}-{{x}}^{{2}},{y}={{x}}^{{2}}-{6}$

Refer the attached image. Graph of y=12-x^2 is plotted in blue color and graph of y=x^2-6 is plotted in red color. The curves intersects at x= $\displaystyle\pm$ 3

Area of the region enclosed by the given curves A= $\displaystyle{\int_{{-{3}}}^{{3}}}{\left({\left({12}-{{x}}^{{2}}\right)}-{\left({{x}}^{{2}}-{6}\right)}\right)}{\left.{d}{x}\right.}$

$\displaystyle{A}={\int_{{-{3}}}^{{3}}}{\left({12}-{{x}}^{{2}}-{{x}}^{{2}}+{6}\right)}{\left.{d}{x}\right.}$

$\displaystyle{A}={2}{\int_{{0}}^{{3}}}{\left({18}-{2}{{x}}^{{2}}\right)}{\left.{d}{x}\right.}$

$\displaystyle{A}={2}{{\left[{18}{x}-{2}\frac{{{x}}^{{3}}}{{3}}\right]}_{{0}}^{{3}}}$

$\displaystyle{A}={2}{\left({18}\cdot{3}-\frac{{2}}{{3}}{\left({{3}}^{{3}}\right)}\right)}$

$\displaystyle{A}={2}{\left({54}-\frac{{54}}{{3}}\right)}$

$\displaystyle{A}={2}{\left(\frac{{108}}{{3}}\right)}$

$\displaystyle{A}={72}$

Notes

Sunday, 1 February 2015

$\displaystyle{y}={12}-{{x}}^{{2}},{y}={{x}}^{{2}}-{6}$ Sketch the region enclosed by the given curves and find its area.

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Is there any personification in "The Tell-Tale Heart"?

Sunday, 1 February 2015

Sketch the region enclosed by the given curves and find its area.

No comments:

Post a Comment

Is there any personification in &quot;The Tell-Tale Heart&quot;?

$\displaystyle{y}={12}-{{x}}^{{2}},{y}={{x}}^{{2}}-{6}$ Sketch the region enclosed by the given curves and find its area.

Is there any personification in "The Tell-Tale Heart"?