The area (in sq. units) of the region (x,y) \in R^{2} ; x^{2} \leq y \leq 3

Engineering

Mathematics

Introduction to Area

Question

The area (in sq. units) of the region (x,y) $\in R^{2}; x^{2} \leq y \leq 3 - 2 x$ , is

$\frac{34}{3}$

$\frac{31}{3}$

$\frac{29}{3}$

$\frac{32}{3}$

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Point of intersection of y = x² & y = – 2x + 3 is

obtained by x² + 2x – 3 = 0

⇒ x = – 3, 1

$So, Area = \int_{- 3}^{1} (3 - 2 x - x^{2}) = 3 (4) - 2 (\frac{1^{2} - 3^{2}}{2}) - (\frac{1^{3} + 3^{3}}{3}) = 12 + 8 - \frac{28}{3} = \frac{32}{3}$