The area of the closed figure bounded by x = − 1 , x = 2 and y = { − x 2 + 2 2 x − 1 , x ≤ 1 x > 1 and the x-axis is

A = ∫ − 1 1 ( − x 2 + 2 ) d x + ∫ 1 2 ( 2 x − 1 ) d x = [ − 3 x 3 + 2 x ] − 1 1 + [ x 2 − x ] 1 2 = 3 10 + 2 = 3 16 .

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Mathematics - Area Under Curves Question with Solution | TestHub

MathematicsArea Under CurvesArea of Curve along axisEasy2 minQB

MathematicsEasysingle choice

The area of the closed figure bounded by $x = - 1, x = 2$ and $y = {- x^{2} + 2 2 x - 1, x \leq 1 x > 1$ and the x-axis is

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$A = \int_{- 1}^{1} (- x^{2} + 2) d x + \int_{1}^{2} (2 x - 1) d x = [- \frac{x ^{3}}{3} + 2 x]_{- 1}^{1} + [x^{2} - x]_{1}^{2} = \frac{10}{3} + 2 = \frac{16}{3}$ .

Stream:JEESubject:MathematicsTopic:Area Under CurvesSubtopic:Area of Curve along axis

⏱ 2mℹ️ Source: QB

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