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The area bounded by the x-axis, the curv...

The area bounded by the x-axis, the curve `y=f(x),` and the lines `x=1,x=b` is equal to `sqrt(b^2+1)-sqrt(2)` for all `b >1,` then `f(x)` is `sqrt(x-1)` (b) `sqrt(x+1)` `sqrt(x^2+1)` (d) `x/(sqrt(1+x^2))`

A

`sqrt(x-1)`

B

`sqrt(x+1)`

C

`sqrt(x^(2)+1)`

D

`x/(sqrt(x^(2)+1))`

Text Solution

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The correct Answer is:
D
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ML KHANNA-AREA OF CURVES-SELF ASSESSEMENT TEST
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  2. The value(s) ofint(0)^(1)(x^(4)(1-x)^(4))/(1+x^(2)) dx is (are)

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  3. The value of the integral overset(pi//2)underset(-pi//2)int{x^(2)+lo...

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  4. The value of int (sqrt ( log 2 )) ^(sqrt( log 3 )) (x sin x ^(2))/( si...

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  5. int(0)^(pi)[cotx]dx, where [.] denotes the greatest integer function, ...

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  6. Let p(x) be a function defined on R such that p'(x)=p'(1-x) for all x ...

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  7. If g(x)=int(0)^(x)cos^(4)t dt, then g(x+pi) equals

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  8. Let f be a non-negative function defined on the interval[0,1]. If int(...

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

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

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

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

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

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  14. The value of underset(xrarr0)(lim)(1)/(x^(3)) int(0)^(x)(tln(1+t))/(t^...

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  15. 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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  16. For any real number x, let [x]= largest integer less than or equalto x...

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

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