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Mathematics - Area Under Curves Question with Solution | TestHub

MathematicsArea Under CurvesArea bounded by Miscellaneous CurvesHard2 minQB

MathematicsHardmultiple choice

Let $A$ be the area between $2 {y} = ⌊ x ⌋ + 1$ , the $x$ -axis, and $x^{2} - x < 0$ , with $0 < y < 1$ . Which upper bounds for $A$ are valid?

Options:(select one or more)

Answer:

A, B, C

Solution:

Since x^2 - x < 0 gives 0 < x < 1, we have floor(x) = 0 and y = 1/2. Hence A = 1/2. Among the listed options, the values that are upper bounds for A are pi/6, 3/4, and 1/2; 1/3 is not an upper bound. Therefore the valid choices are A, B, and C.

Stream:JEESubject:MathematicsTopic:Area Under CurvesSubtopic:Area bounded by Miscellaneous Curves

⏱ 2mℹ️ Source: QB

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