Question
Download Solution PDFThe area enclosed by the curves y = x - 1 and y2 = 2x + 6 is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
Given curves are y = x - 1 and y2 = 2x + 6
On solving, we get,
y2 = 2(y + 1) + 6
⇒ y2 - 2y - 8 = 0
⇒ (y - 4)(y + 2) = 0
⇒ y = -2, 4
Now, we can find the area by
A = \(\int_{-2}^{4}\left [y+1-\left ( \frac{y^{2}}{2}-3 \right ) \right ]dy \)
= \(\int_{-2}^{4}\left (4+y-\frac{y^{2}}{2} \right )dy \)
= \(\left [ 4y+\frac{y^{2}}{2} -\frac{y^{3}}{6}\right ]_{-2}^{4}\)
= \(16+8-\frac{32}{3}-\left ( -8+2+\frac{4}{3} \right )\)
∴ A = 18
Last updated on May 26, 2025
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