Question

Draw a rough sketch and find the area bounded by the curve x² = y and x + y = 2.

Answer 1

The given curves are: x² = y

Which is an upward parabola with vertex at origin

And line x + y = 2 ⇒ y = 2 – x

x² = 2 – x

⇒ x² + x – 2 = 0 

⇒ (x + 2)(x – 1) = 0 

⇒ x = -2 and x = 1 

Now, y = 2-(-2) = 4 

and y = 2 – 1 ⇒ y = 1 

⇒ y = 4 and y = 1 

Thus, the points of intersection are (-2, 4) and (1, 1) 

Required area of shaded region