<p><strong>Area Enclosed by Curves Projected to The $x$-Axis.</strong></p>
<p>The area bounded by two curves, $y = \mathrm{f}(x)$ and $y = \mathrm{g}(x)$, where $\mathrm{f}(x) \geq \mathrm{g}(x)$, from $x = a$ to $x = b$, where $a &lt; b$, is given by $\displaystyle\int\nolimits_{a}^{b} [\mathrm{f}(x) - \mathrm{g}(x)] \, \mathrm{d}x$.</p>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1768713371331-uxuh094b7c.png" style="max-width: min(500px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<p>Note: For area between curves, there will not be any negative area generated as we are finding the area between the curves. </p>
<p style="margin-top: 1.5rem"><strong>Area Enclosed by Curves Projected to The $y$-Axis.</strong></p>
<p>The area bounded by two curves, ${x=\mathrm{f}(y)}$ and ${x=\mathrm{g}(y)}$, where ${\mathrm{f}(y) \geq \mathrm{g}(y)}$, from ${y=a}$ to ${y=b}$, where ${a &lt; b}$, is given by ${\displaystyle\int\nolimits_{a}^{b} [\mathrm{f}(y) - \mathrm{g}(y)] \mathrm{d}y.}$</p>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1768713520724-5lvqnpm2dyj.png" style="max-width: min(500px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>

**Area Enclosed by Curves Projected to The $x$-Axis.**

The area bounded by two curves, $y = \mathrm{f}(x)$ and $y = \mathrm{g}(x)$, where $\mathrm{f}(x) \geq \mathrm{g}(x)$, from $x = a$ to $x = b$, where $a < b$, is given by $\displaystyle\displaystyle \displaystyle\int\nolimits_{a}^{b} [\mathrm{f}(x) - \mathrm{g}(x)] \, \mathrm{d}x$.

Note: For area between curves, there will not be any negative area generated as we are finding the area between the curves. 

**Area Enclosed by Curves Projected to The $y$-Axis.**

The area bounded by two curves, ${x=\mathrm{f}(y)}$ and ${x=\mathrm{g}(y)}$, where ${\mathrm{f}(y) \geq \mathrm{g}(y)}$, from ${y=a}$ to ${y=b}$, where ${a < b}$, is given by ${\displaystyle\displaystyle \displaystyle\int\nolimits_{a}^{b} [\mathrm{f}(y) - \mathrm{g}(y)] \mathrm{d}y.}$

Area Between Two Curves

Area Between Two Curves

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