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Consider the function defined implicity ...

Consider the function defined implicity by the equation `y^(2)-2ye^(sin^(-1)x)+x^(2)-1+[x]+e^(2sin ^(-1)x)=0("where [x] denotes the greatest integer function").`
Line x=0 divides the region mentioned above in two parts. The ratio of area of left-hand side of line to that of right-hand side of line is

A

`1+pi:pi`

B

`2-pi:pi`

C

`1:1`

D

`pi+2:pi`

Text Solution

Verified by Experts

The correct Answer is:
D
`"Ratio "=((pi)/(2)+1)/((pi)/(2))=(pi+2)/(pi).`
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CENGAGE-AREA-Exercise (Comprehension)
  1. Let A(r) be the area of the region bounded between the curves y^(2)=(e...

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  2. If y=f(x) is a monotonic function in (a,b), then the area bounded by t...

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  3. If y=f(x) is a monotonic function in (a,b), then the area bounded by t...

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  4. If y=f(x) is a monotonic function in (a,b), then the area bounded by t...

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  5. Consider the area S(0),S(1),S(2)…. bounded by the x-axis and half-wave...

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  6. Consider the sequence of natural numbers s0,s1,s2,... such that s0 =3,...

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  7. Consider the area S(0),S(1),S(2)…. bounded by the x-axis and half-wave...

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  8. "Two curves "C(1)equiv[f(y)]^(2//3)+[f(x)]^(1//3)=0 ...

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  9. Two curves C(1)equiv[f(y)]^(2//3)+[f(x)]^(1//3)=0 and C(2)equiv[f(y)]^...

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  10. Two curves C(1)equiv[f(y)]^(2//3)+[f(x)]^(1//3)=0 and C(2)equiv[f(y)]^...

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  11. Consider the two curves C(1):y=1+cos x and C(2): y=1 + cos (x-alpha)" ...

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  12. Consider two curves C1:y =1/x and C2.y=lnx on the xy plane. Let D1, de...

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  13. Consider the function defined implicity by the equation y^(2)-2ye^(sin...

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  14. Consider the function defined implicity by the equation y^(2)-2ye^(sin...

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  15. Consider two functions f(x)={([x]",",-2le x le -1),(|x|+1",",-1 lt x...

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  16. Computing area with parametrically represented boundaries : If the bou...

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  17. Computing area with parametrically represented boundaries : If the bou...

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  18. Computing area with parametrically represented boundaries : If the bou...

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  19. Let f(x) be a continuous function fiven by f(x)={(2x",", |x|le1),(x^(2...

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  20. Let f(x) be continuous function given by f(x)={2x ,|x|lt=1x^2+a x+b ,|...

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