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The area of the plane region bounded by ...

The area of the plane region bounded by the curves `x + 2y^(2)=0` and `x+3y^(2)=1` is equal to

A

`(4)/(3)` sq units

B

`(5)/(3)` sq unit

C

`(1)/(3)` sq unit

D

`(2)/(3)` sq unit

Text Solution

Verified by Experts

The correct Answer is:
A
On solving the given curves, we get
`y=pm1 and x=-2`
`therefore` Intersection points are (-2,1) and (-2,-1)
`therefore` Required area `=|int_(-1)^(1)(1-3y^(2)-2y^(2))dy|`

`=|2int_(0)^(1)(1-y^(2))dy|=|2[y-(y^(3))/(3)]_(0)^(1)|=(4)/(3)` sq units
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-APPLICATIONS OF DEFINITE INTEGRALS -Exercise 2
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  2. The area of the figure bounded by the curves y^(2)=2x+1 and x-y-1=0 , ...

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  3. The area of the plane region bounded by the curves x + 2y^(2)=0 and x+...

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  4. The area enclosed between the curves y = x^(3) and y = sqrt(x) is

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  5. The area enclosed between the parabola y = x^(2)-x+2 and the line y = ...

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  6. The area bounded by the curves y^(2)=4a^(2)(x-1) and lines x = 1 and y...

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  7. The area bounded by the curves y = cos x and y = sin x between the ord...

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  8. The area of the plane region bounded by the curve x = y^(2)-2 and the ...

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  9. The area bounded by the curve y = 2x - x^(2) and the line y = - x is

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  10. For 0 lt= x lt= pi, the area bounded by y = x and y = x + sin x, is

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  11. If the area above the x-axis, bounded by the curves y = 2^(kx) and x =...

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  12. The area of the region described by A = {(x,y) : x^2 + y^2 lt= 1and y^...

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  13. The area in the first quadrant between x^2+y^2=pi^2 and y=sinx is

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  14. The area bounded by the curves y=sqrtx, 2y-x+3=0, X-axis and lying in ...

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  15. The area bounded by y = |sin x|, X-axis and the line |x|=pi is

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  16. Find the area bounded by the x-axis, part of the curve y=(1-8/(x^2)) ,...

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  17. The area bounded by the graph of y=f(x), f(x) gt0 on [0,a] and x-axis ...

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  18. The line x = (pi)/(4) divides the area of the region bounded by y = si...

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

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  20. The area (in sq units) of the region bounded by the curves y = e^(x), ...

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