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 $S_{1}, S_{3}$ and the line $x = 3$ 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 $B (1, - 1)$ . Area $= \int_{1}^{3} (x^{2} - 4 x - 3) d x = [\frac{x ^{3}}{3}]_{1}^{3} - [\frac{( 4 x - 3 ) ^{3/2}}{6}]_{1}^{3} =$ $\frac{26}{3} - \frac{26}{6} = \frac{13}{3} .$

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

⏱ 2mℹ️ Source: QB

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