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Prove that area common to ellipse (x^2)/...

Prove that area common to ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` and its auxiliary circle `x^2+y^2=a^2` is equal to the area of another ellipse of semi-axis `aa n da-bdot`

A

`(a+b)^(2)tan^(-1(b)/(a)`

B

`(a+b)^(2)tan^(-1(a)/(b)`

C

`4abtan^(-1)(b)/(a)`

D

`4abtan^(-1)(a)/(b)`

Text Solution

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The correct Answer is:
C
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DISHA PUBLICATION-APPLICATION OF INTEGRALS-EXERCISE-1: CONCEPT BUILDER (TOPICWISE)
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  2. The area of the region bounded by the parabola (y-2)^(2) = x- 1, the t...

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  3. Find the area lying in the first quadrant and bounded by the curve y=x...

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  4. Area bounded by the circle x^(2) + y^(2)= 1 and the curve |x| + |y|=1 ...

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  5. A O B is the positive quadrant of the ellipse (x^2)/(a^2)+(y^2)/(b^...

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  6. Find the area enclosed between the curves: y = loge (x + e) , x = loge...

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  7. Find the area bounded by the curves x^2+y^2=25 ,4y=|4-x^2|, and x=0 ab...

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  8. The area bounded by the curves y=x e^x ,y=x e^(-x) and the line x=1 is...

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  9. Using the method of integration find the area of the triangle ABC, ...

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  10. If y=f(x) makes positive intercepts of 2 and 1 unit on x and y-coordin...

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  11. The parabolas y^(2)=4x and x^(2)=4y divide the square region bounded b...

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  12. The area bounded by the curve y^(2)(a^(2)+ x^(2))= x^(2)(a^(2)- x^(2...

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  13. Prove that area common to ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 and its au...

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  14. If C(1) equiv y = 1/(1+x^(2)) and C(2) equiv y =x^(2) / 2 be two curve...

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  15. The area bounded by y = x^(2) + 3 and y= 2x + 3 is (in sq. units)

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  16. The area bounded by the curves y = x e^(x), = x e^(-x) and the line ...

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  17. The area bounded by the curve y=x^(2), the normal at (1, 1) and the x-...

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  18. Find the area bounded by the y-axis, y=cosx ,a n dy=sinxw h e n0lt=xlt...

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  19. Find the area bounded by curves (x-1)^2+y^2=1and x^2+y^2=1.

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  20. f(x) = min{2 sinx, 1- cos x, 1} then int0^(pi)f(x) dx is equal to

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