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Prove that area of the smaller part of t...

Prove that area of the smaller part of the cirlce `x ^(2) + y ^(2) =a ^(2)` cut off by the line `x = (a)/(sqrt2)` is `(a ^(2))/( 4) (pi-2)` sq. units.

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MODERN PUBLICATION-APPLICATIONS OF THE INTEGRALS -EXERCISE 8 (A)
  1. Find the area under the curve y =(x^2 + 2)^2 + 2x between the ordinate...

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  2. Find the area of the region in the first quadrant enclosed by x-axis,...

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  3. Prove that area of the smaller part of the cirlce x ^(2) + y ^(2) =a ^...

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  4. Determine the area under the curve y=sqrt(a^(2)-x^(2)) included betwee...

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  5. Determine the area enclosed between the curve y= cos 2x, 0 le x le (pi...

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  6. Calculate the area bounded by the curve: f (x)= sin ^(2) "" (x)/(2),...

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  7. Draw a rough sketch of the curve y = cos^2 x in [0, 1] and find the ar...

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  8. (i) Make a rough sketch of the graph of the function y = sin x, 0 le x...

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  9. Make a rough sketch of the graph of the function y =2 sin x, 0 le x le...

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  10. (i) Draw a rough sketch of y = sin 2x and determine the area enclosed...

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  11. Make a rough sketch of the graph of y = cos ^(2) x, 0 le x le (pi)/(2)...

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  12. Find the area bounded by the cirxle x^2+y^2 =16 and the line y=x in th...

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  13. Find the area of the smaller part of the circle x^2+y^2=a^2cut off by...

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  14. Find the area under the given curves and given lines:(i) y=x^2,x = 1,...

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  15. Draw the rough sketch of y^2+1=x ,\ xlt=2. Find the area enclosed by t...

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  16. Find the area of the region bounded by the ellipse : (a) (x ^(2))/( ...

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  17. Find the area between the curve (x ^(2))/( a ^(2)) + (y ^(2))/(b ^(2))...

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  18. Find the area of the region bounded by the ellipse x^2 / a^2 + y^2 / b...

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  19. Sketch the region {(x,y): 4x ^(2) + 9y ^(2) = 36} and find its area, u...

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  20. Find the area bounded by the circle x 2 + y2 = 16 and the line 3y...

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