If the area bounded by the curve y = x − x 2 and the line y = m x equals 2 9 , then the value of m is

Intersections: x − x 2 = m x ⇒ x = 0 , x = 1 − m . Area = ∫ 0 1 − m ( ( 1 − m ) x − x 2 ) d x = 6 ∣1 − m ∣ 3 = 2 9 ⇒ ∣1 − m ∣ = 3 ⇒ m = − 2 or m = 4 .

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Mathematics - Area Under Curves Question with Solution | TestHub

MathematicsArea Under CurvesArea bounded by two curvesMedium2 minQB

MathematicsMediummultiple choice

If the area bounded by the curve $y = x - x^{2}$ and the line $y = m x$ equals $\frac{9}{2}$ , then the value of $m$ is

Options:(select one or more)

Answer:

B, D

Solution:

Intersections: $x - x^{2} = m x \Rightarrow x = 0, x = 1 - m$ . Area $= \int_{0}^{1 - m} ((1 - m) x - x^{2}) d x = \frac{∣1 - m ∣ ^{3}}{6} =$ $\frac{9}{2} \Rightarrow ∣1 - m ∣ = 3 \Rightarrow m = - 2$ or $m = 4$ .

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

⏱ 2mℹ️ Source: QB

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