The area of the region bounded by y – x = 2 and x^2 = y is equal to :- (1) 16/3 (2) 2/3 (3) 9/2 (4) 4/3

Question

The area of the region bounded by y – x = 2 and x² = y is equal to :-

(1) \(\frac{16}{3}\)

(2) \(\frac{2}{3}\)

(3) \(\frac{9}{2}\)

(4) \(\frac{4}{3}\)

Answer 1

Correct option (3) \(\frac{9}{2}\).

y – x = 2 , x² = y 

Now, x² = 2 + x

\(\Rightarrow\) x² – x – 2 = 0 

(x + 1)(x-2) = 0

Area = \(\int\limits_{-1}^2\) (2+x-x²)