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Let f:[-1,2]vec[0,oo) be a continuous fu...

Let `f:[-1,2]vec[0,oo)` be a continuous function such that `f(x)=f(1-x)fora l lx in [-1,2]dot` Let `R_1=int_(-1)^2xf(x)dx ,` and `R_2` be the area of the region bounded by `y=f(x),x=-1,x=2,` and the `x-a xi s` . Then `R_1=2R_2` (b) `R_1=3R_2` `2R_1` (d) `3R_1=R_2`

A

`R_(1)=2R_(2)`

B

`R_(1)=3R_(2)`

C

`2R_(1)=R_(2)`

D

`3R_(1)=R_(2)`

Text Solution

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The correct Answer is:
C
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ARIHANT MATHS-AREA OF BOUNDED REGIONS-Exercise (Questions Asked In Previous 13 Years Exam)
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  2. Let S be the area of the region enclosed by y=e^-x^2,y=0,x=0,a n dx=1....

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  3. Let f:[-1,2]vec[0,oo) be a continuous function such that f(x)=f(1-x)fo...

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  4. Let the straight line x= b divide the area enclosed by y=(1-x)^(2),y=0...

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  5. Area of the region bounded by the curve y=e^(x) and linesx=0 and y=e i...

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  6. The area of the region bounded by the curves y=sqrt[[1+sinx]/cosx] and...

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  7. Consider the function defined implicitly by the equation y^3-3y+x=0 on...

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  8. Consider the function defined implicitly by the equation y^3-3y+x=0 on...

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  9. Consider the function defined implicitly by the equation y^3-3y+x=0 on...

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  10. The area (in sqaure units) of the region {(x,y):x ge 0, x + y le 3, x^...

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  11. The area (in sq units) of the region {(x, y) : y^2 gt= 2x and x^2 + y^...

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  12. The area (in sq units) of the region described by {(x,y):y^(2)le2x and...

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  13. The area (in sq. units) of the quadrilateral formed by the tangents...

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

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  15. The area (in square units) bounded by the curves y=sqrt(x),2y-x+3=0, x...

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  16. The area bounded between the parabola x^(2)=y/4 and x^(2)=9y and the s...

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  17. The area of the region enclosed by the curves y=x, x=e,y=(1)/(x) and t...

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  18. The area bounded by the curves y=cosx and y=sinx between the ordinates...

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  19. The area of the region bounded by the parabola (y-2)^(2) = x- 1, the t...

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  20. The area of the plane region bounded by the curves x""+""2y^2=""0 and ...

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