Mathematics - Area Under Curves Question with Solution | TestHub

MathematicsArea Under CurvesArea bounded by two curvesMedium2 minQB

MathematicsMediumsingle choice

Passage / Comprehension

Let the curves be $S_{1} : y = x^{2}, S_{2} : y = - x^{2}, S_{3} : y^{2} = 4 x - 3$ .

Area bounded by the curves $S_{1}, S_{2}, S_{3}$ is

Options:

Answer:

Solution:

$S_{1}$ meets $S_{3}$ where $x^{4} = 4 x - 3$ , i.e. $(x - 1)^{2} (x^{2} + 2 x + 3) = 0$ , so only at $x = 1 : S_{3}$ touches $S_{1}$ at $A (1, 1)$ , and by symmetry touches $S_{2}$ at $B (1, - 1)$ . Region $O A B$ : for $0 \leq y \leq 1$ the left boundary is $x = y$ and the right boundary is $x = \frac{y ^{2} + 3}{4}$ . Area $= 2 \int_{0}^{1} (\frac{y ^{2} + 3}{4} - y) d y = 2 [\frac{1}{12} + \frac{3}{4} - \frac{2}{3}] = \frac{1}{3}$ .

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

⏱ 2mℹ️ Source: QB

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