The area bounded by the curve y=x∣x∣, x-axis and the ordinates x=−1and x=1is given by(A) 0 (B) 31 (C) 32 (D) 34[Hint : y=x2if x>0and y=−x2if x<0].

Solution: area=∫−10ydx+∫01ydx=∫−10−x2dx+∫01x2dx=(−3x3)−10+(3x3)01=∣∣−31∣∣+31=32unit2

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Question

The area bounded by the curve $y = x ∣ x ∣$ , x-axis and the ordinates $x = - 1$ and $x = 1$ is given by(A) 0 (B) $\frac{1}{3}$ (C) $\frac{2}{3}$ (D) $\frac{4}{3}$ [Hint : $y = x^{2}$ if $x > 0$ and $y = - x^{2}$ if $x < 0$ ].

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The area bounded by the curve

y = x ∣ x ∣

, x-axis and the ordinates

x = - 1

and

x = 1

is given by(A) 0 (B)

\frac{1}{3}

(C)

\frac{2}{3}

(D)

\frac{4}{3}

[Hint :

y = x^{2}

x > 0

and

y = - x^{2}

x < 0

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Solution: area=

\int_{- 1}^{0} y d x + \int_{0}^{1} y d x

\int_{- 1}^{0} - x^{2} d x + \int_{0}^{1} x^{2} d x

(- \frac{x ^{3}}{3})_{- 1}^{0} + (\frac{x ^{3}}{3})_{0}^{1}

∣ ∣ - \frac{1}{3} ∣ ∣ + \frac{1}{3}

\frac{2}{3} u n i t^{2}

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Question Text	The area bounded by the curve $y = x ∣ x ∣$ , x-axis and the ordinates $x = - 1$ and $x = 1$ is given by(A) 0 (B) $\frac{1}{3}$ (C) $\frac{2}{3}$ (D) $\frac{4}{3}$ [Hint : $y = x^{2}$ if $x > 0$ and $y = - x^{2}$ if $x < 0$ ].
Answer Type	Text solution:1
Upvotes	150