If the area of the region { ( x , y ) : 1 + x 2 ≤ y ≤ min { x + 7 , 11 − 3 x } } is A , then 3 A is equal to

A = ∫ − 2 1 ( x + 7 − x 2 − 1 ) d x + ∫ 1 2 ( 11 + 3 x − x 2 − 1 ) d x = [ 2 x 2 + 6 x − 3 x 3 ] − 2 1 + [ 10 x − 2 3 x 2 − 3 x 3 ] 1 2 = 3 50 ⇒ 3 A = 50 Option (1)

Mathematics - Area Under Curves Question with Solution | TestHub

MathematicsArea Under CurvesArea bounded by two curvesMedium2 minPYQ_2025

MathematicsMediumsingle choice

If the area of the region ${(x, y) : 1 + x^{2} \leq y \leq min {x + 7, 11 - 3 x}}$ is A , then 3 A is equal to

Options:

Answer:

Solution:

$A = \int_{- 2}^{1} (x + 7 - x^{2} - 1) d x + \int_{1}^{2} (11 + 3 x - x^{2} - 1) d x = [\frac{x ^{2}}{2} + 6 x - \frac{x ^{3}}{3}]_{- 2}^{1} + [10 x - \frac{3 x ^{2}}{2} - \frac{x ^{3}}{3}]_{1}^{2} = \frac{50}{3} \Rightarrow 3 A = 50 Option (1)$

Stream:JEESubject:MathematicsTopic:Area Under CurvesSubtopic:Area bounded by two curves

⏱ 2mℹ️ Source: PYQ_2025

Doubts & Discussion

Loading discussions...