SATHEE: Area Question 9

Area Question 9

Question 9

The area (in sq units) of the region bounded by the parabola, $y = x^{2} + 2$ and the lines, $y = x + 1, x = 0$ and $x = 3$ , is

(2019 Main, 12 Jan I) (a) $\frac{15}{2}$ (b) $\frac{17}{4}$ (c) $\frac{21}{2}$ (d) $\frac{15}{4}$

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Solution:

Given equation of parabola is $y = x^{2} + 2$ , and the line is $y = x + 1$

The required area $=$ area of shaded region $= \int_{0}^{3} ((x^{2} + 2) - (x + 1)) d x = \int_{0}^{3} (x^{2} - x + 1) d x$

$= \frac{x^{3}}{3} - \frac{x^{2}}{2} + x^{3} = \frac{27}{3} - \frac{9}{2} + 3 - 0$

$= 9 - \frac{9}{2} + 3 = 12 - \frac{9}{2} = \frac{15}{2}$ sq units

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Area Question 9

Question 9

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