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The area bounded by the curve y=x |x|, x...

The area bounded by the curve `y=x |x|`, `x`-axis and the ordinates `x=-1` & `x=1` is:

A

0

B

`(1)/(3)`

C

`(2)/(3)`

D

`(4)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
C
Given, `y=x|x|={(" "x^(2)","x ge0),(-x^(2)","x lt0):}`

` :. ` Required area `=2 int_(0)^(1)x|x|=2 int_(0)^(1)x^(2)dx`
`=2[(x^(3))/(3)](0)^(1)=(2)/(3)(1^(3)-0^(3))`
`=(2)/(3)` sq. unit.
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NAGEEN PRAKASHAN ENGLISH-APPLICATIONS OF INTEGRALS-Miscellaneous Exercise
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  9. Find the area of the smaller region bounded by the ellipse (x^2)/(a^2)...

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  17. The area bounded by the curve y=x |x|, x-axis and the ordinates x=-1 &...

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  18. The area of the circle x^2+y^2=16exterior to the parabola y^2=6xis(A) ...

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