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Find the area of the region bounded by t...

Find the area of the region bounded by the curve `y=x^2` and `y=sec^(-1)[-sin^(2)x]`, where [.] denotes the greatest integer function.

A

`(1)/(3)(4-pi)^(3//2)`

B

`(8(4-pi)^(3//2)`

C

`(8)/(3)(4-pi)^(3//2)`

D

`(8)/(3)(4-pi)^(1//2)`

Text Solution

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The correct Answer is:
C
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OBJECTIVE RD SHARMA ENGLISH-AREAS OF BOUNDED REGIONS-Exercise
  1. Find the area of the region bounded by the parabola "x"^2=4"y\ " an...

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  2. Find the area lying in the first quadrant and bounded by the curve y=x...

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  3. The area of the region (in square units) bounded by the curve x^2=4y a...

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  4. The area bounded by the x-axis and the curve y = 4x - y^(2) - 3 id

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  5. Find the area of the region enclosed by the parabola y^2=4a x\ a n d t...

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  6. The area bounded by y = tan x, y = cot x, X-axis in 0 lt=x lt= pi/2 is

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  7. Area lying between the curves y^2=4x and y = 2x is:

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  8. Area common to the circle x^2+y^2=64 and the parabola y^2=4x is

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  9. The area of the figure bounded by |y|=1-x^(2) is in square units,

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  10. Find the area of the figure bounded by the parabolas x=-2y^2, x=1-3y^2...

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  11. The area bounded by y = x |sinx| and x - axis between x = 0, x = 2pi i...

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  12. Find the area bounded by the curve y=2x-x^(2), and the line y=x

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  13. Find the area bounded by the curve y=(x-1)(x-2)(x-3) lying between the...

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  14. Area common to the curves y=sqrt(x) and x=sqrt(y) is (A) 1 (B) 2/3 (C)...

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  15. Find the equation of common tangent of y^(2)=4axandx^(2)=4by.

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  16. Area of the region bounded by [x] ^(2) =[y] ^(2), if x in [1,5], where...

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  17. If A denotes the area bounded by f(x)=|("sin"x + "cos"x)/(x)|, X-axis,...

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  18. Find the area of the region bounded by the curve y=x^2 and y=sec^(-1)[...

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  19. The area the region included between the region satisfying min (/x//,/...

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  20. If f(x) ge 0, AA x in (0,2) and y=f(x) makes positive intercepts of 2 ...

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