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The area enclosed between the curve `y^2(2a-x)=x^3` and the line `x=2` above the `x-a xi s` is `pia^2s qdotu n i t s` (b) `(3pia^2)/2s qdotu n i t s` `2pia^2s qdotu n i t s` (d) `3pia^2s qdotu n i t s`

A

`pia^(2)`

B

`3//2 pia^(2)`

C

`2pia^(2)`

D

`3pia^(2)`

Text Solution

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The correct Answer is:
B
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The area enclosed between the curve y^2(2a-x)=x^3 and the line x=2a above the x-axis is (a) pia^2s qdotu n i t s (b) (3pia^2)/2s qdotu n i t s (c) 2pia^2s qdotu n i t s (d) 3pia^2s qdotu n i t s

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Let f(x)=x^3+3x+2a n dg(x) be the inverse of it. Then the area bounded by g(x) , the x-axis, and the ordinate at x=-2a n dx=6 is (a) 9/4s qdotu n i t s (b) 4/3s qdotu n i t s (c) 5/4s qdotu n i t s (d) 7/3s qdotu n i t s

The area of the smaller region bounded by circle x^2+y^2=1 and |y|=x+1 (a) pi/2-1/2s qdotu n i t s (b) pi/2-1s qdotu n i t s (c) pi/2s qdotu n i t s (d) pi/2 +1s qdotu n i t s

The area bounded by the two branches of curve (y-x)^2=x^3 and the straight line x=1 is (a) 1/5s qdotu n i t s (b) 3/5s qdotu n i t s 4/5s qdotu n i t s (d) 8/4s qdotu n i t s

Consider two curves C_1: y^2=4[sqrt(y)]x a n dC_2: x^2=4[sqrt(x)]y , where [.] denotes the greatest integer function. Then the area of region enclosed by these two curves within the square formed by the lines x=1,y=1,x=4,y=4 is (a) 8/3s qdotu n i t s (b) (10)/3s qdotu n i t s (c) (11)/3s qdotu n i t s (d) (11)/4s qdotu n i t s

The area of the region whose boundaries are defined by the curves y= 2cosx , y= 3tanx and the y-axis is (a) 1+31n(2/(sqrt(3)))s qdotu n i t s (b) 1+3/2 1n3-31n2s qdotu n i t s (c) 1+3/2 1n3-1n2s qdotu n i t s (d) 1n3-1n2s qdotu n i t s

OBJECTIVE RD SHARMA ENGLISH-AREAS OF BOUNDED REGIONS-Chapter Test
  1. If the area bounded by the curve y=f(x), x-axis and the ordinates x=1 ...

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

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

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  4. The area bounded by the curve y=4x-x^2 and x-axis is (A) 30/7 sq. unit...

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  5. Area bounded by the parabola y^2=x and the line 2y=x is:

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  6. Area between the x-axis and the curve y=cosx, when 0 le x le 2pi is:

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  7. The ratio of the areas between the curves y=cosx and y=cos2x and x-axi...

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  8. Find the area bounded by the parabola y=x^2+1 and the straight line x+...

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  9. Prove that the area common to the two parabolas y=2x^2\ a n d\ y=x^2+4...

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  10. Find the area of the region {(x,y): x^(2)+y^(2) le 1 le x + y}

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  11. Find the area bounded by the parabola y^2 = 4ax and its latus rectum.

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  12. The area bounded by the curve y=x^(4)-2x^(3)+x^(2)+3 with x-axis and o...

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  13. Find the area common to two parabolas x^2=4ay and y^2=4ax, using integ...

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  14. The area (in square units) bounded by curves y=sinx between the ordin...

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

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  16. The area enclosed between the curves y=log(e)(x+e),x=log(e)((1)/(y)), ...

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  17. Find the area of the region formed by x^(2)+y^(2)-6x-4y+12 le 0, y le ...

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  18. If An be the area bounded by the curve y=(tanx)^n and the lines x=0,\ ...

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  19. The area bounded by the parabola y^2 = x, straight line y = 4 and y-ax...

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  20. The area (in square units), bounded by y=2-x^(2) and x+y=0 , is

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