Find the area of the region enclosed between the parabola $y=x^{2}$ and the line $y=4$.

Find the area of the region enclosed between the parabola y=x² and the line y=4.

Exercises · Q11

y=x^{2}

Maharashtra MsbshseTextbookSubjectiveImportance★★★★★

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Step 1 — find the intersection points. Set the curves equal:

x^{2}=4\ \Rightarrow\ x=\pm 2

So the limits are $a=-2$ and $b=2$ .

Step 2 — decide which is on top. Test $x=0$ : the line gives $y=4$ , the parabola gives $y=0$ . The line $y=4$ is above the parabola $y=x^{2}$ on $(-2,2)$ , so upper $=4$ , lower $=x^{2}$ .

Step 3 — integrate the difference.

A=\int_{-2}^{2}(4-x^{2})\,dx = \left[4x-\frac{x^{3}}{3}\right]_{-2}^{2}

$\text{At }x=2:\ 4(2)-\frac{2^{3}}{3}=8-\frac{8}{3}=\frac{24-8}{3}=\frac{16}{3}$ …

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Q.Find the area of the region enclosed between the parabola $y=x^{2}$ and the line $y=4$ .

Concept understanding — Area between Two Curves

Q.Find the area of the region enclosed between the parabola y=x2y=x^{2}y=x2 and the line y=4y=4y=4.

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Q.Find the area of the region enclosed between the parabola $y=x^{2}$ and the line $y=4$ .

Unlock everything free for 14 days