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If f(x) ge 0, AA x in (0,2) and y=f(x) m...

If `f(x) ge 0, AA x in (0,2)` and `y=f(x)` makes positive intercepts of 2 and 1 units on X and Y -axes respectively and encloses an area of `3/4` unit with axes, then `int_(0)^(2) xf'(x)dx` is

A

`3/2`

B

1

C

`5/4`

D

`(-3)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
d
Clearly, `y=f(x)` passes through (2,0) and (0,1). `therefore o=f(2)and 1=f(0)`
Also, `underset(0)overset(2)(int)f(x)dx=3/4" "["Given"]`
`underset(0)overset(2)(int)underset(I)(x)f'underset(II)((x))dx=[xf(x)]_(0)^(2)-underset(0)overset(2)(int)f(x)dx`
`impliesunderset(0)overset(2)(int)xf'(x)=[2f(2)-(0)]-3/4=2xx0-0xx1-3/3=-3/4`
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OBJECTIVE RD SHARMA ENGLISH-AREAS OF BOUNDED REGIONS-Chapter Test
  1. If f(x) ge 0, AA x in (0,2) and y=f(x) makes positive intercepts of 2 ...

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  2. Area bounded by the curves y=|x-1|, y=0 and |x|=2

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  3. The area inside the parabola 5x^2-y=0 but outside the parabola 2x^2-y+...

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  4. The area enclosed between the curve y^(2)(2a-x)=x^(3) and the line x=2...

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  5. Area bounded by the curve x y^2=a^2(a-x) and the y-axis is (pia^2)/2s ...

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  6. The area of the loop of the curve ay^(2)=x^(2)(a-x) is

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  7. find the area common to the circle x^2y^2=16 a^2 and the parabola y^2=...

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  8. The line y=m x bisects the area enclosed by the curve y=1+4x-x^2 and t...

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  9. The area between the curve y=xsin x and x-axis where o le x le 2 pi ,...

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  10. The area bounded by the curves y=e^(x),y=e^(-x) and y=2, is

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  11. The area enclosed by the curves x=a sin^(3)t and y= a cos^(2)t is equa...

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  12. If A(1) is the area enclosed by the curve xy=1, x-axis and the ordinat...

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  13. If area bounded by the curve y^(2)=4ax and y=mx is a^(2)//3 , then the...

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  14. The value of a for which the area between the curves y^(2) = 4ax and x...

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  15. If the area bounded by the curve y=f(x), x-axis and the ordinates x=1 ...

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  16. The area bounded by the curve y = sin2x, axis and y=1, is

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  17. The area between the curve x=-2y^(2)and x=1-3y^(2), is

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  18. The area between the curves y=cosx, x-axis and the line y=x+1, is

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  19. If the area bounded by the curve y=x^2+1 and the tangents to it drawn ...

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  20. The positive value of the parmeter 'a' for which the area of the figur...

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  21. The area in square units bounded by the curves y=x^(3),y=x^(2) and the...

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