The area of the region A = { x , y : 0 ≤ y ≤ x x + 1 and - 1 ≤ x ≤ 1 } in sq. units, is

x x = x 2 , x ≥ 0 - x 2 , x < 0 Area enclosed = ∫ - 1 0 - x 2 + 1 d x + ∫ 0 1 x 2 + 1 d x = - x 3 3 + x - 1 0 + x 3 3 + x 0 1 = 2

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Mathematics - Area Under Curves Question with Solution | TestHub

MathematicsArea Under CurvesArea bounded by two curvesEasy2 minPYQ_2019

MathematicsEasysingle choice

The area of the region $A = {(x, y) : 0 \leq y \leq x |x| + 1 and - 1 \leq x \leq 1}$ in sq. units, is

Question diagram: The area of the region A = { x , y : 0 ≤ y ≤ x x + 1 and - 1

Options:

Answer:

Solution:

$x |x| = \{\begin{cases} x^{2}, x \geq 0 \\ - x^{2}, x < 0 \end{cases}$

Area enclosed $= \int_{- 1}^{0} (- x^{2} + 1) d x + \int_{0}^{1} (x^{2} + 1) d x$

$= {[- \frac{x^{3}}{3} + x]}_{- 1}^{0} + {[\frac{x^{3}}{3} + x]}_{0}^{1}$

$= 2$

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

⏱ 2mℹ️ Source: PYQ_2019

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