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(i) Show that the areas under the curves...

(i) Show that the areas under the curves `f(x)=cos^2x` and `f(x)=sin^2x` between x=0 and `x=pi` are 1:1.

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MODERN PUBLICATION-APPLICATIONS OF THE INTEGRALS-EXERCISE
  1. Calculate the area of the region enclosed between the circles: (iii) x...

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  2. Calculate the area of the region enclosed between the circles: (iv) (x...

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  3. (i) Show that the areas under the curves f(x)=cos^2x and f(x)=sin^2x b...

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  4. (ii) Compare the areas under the curves y=cos^2x and y=sin^2x between ...

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  5. (a) (i)Find the area of the circle x^2+y^2=16, which is exterior to th...

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  6. Find the area of the circle 4x^2 + 4y^2 = 9 which is interior to the p...

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  7. (b) Find the area of the region bounded by the circle x^2+y^2=16 and t...

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  8. find the area of region founded by the circle x^(2)+y^(2)=1 and line x...

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  9. Make a rough sketch of the region given below and find its area, using...

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  10. Calculate the area enclosed in the region: (iii) {(x,y):x^2+y^2le16,x^...

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  11. Calculate the area enclosed in the region: (iv) {(x,y):y^2le6ax,x^2+y^...

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  12. Draw the rough sketch and find the area of the region: (i){(x,y):x^2 <...

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  13. Draw the rough sketch and find the area of the region : {(x, y) : 4 x^...

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  14. Find the area of the region {(x,y) : 0leylex^2 + 1, 0leylex+1, 0lexle2...

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  15. Draw the rough sketch and find the area of the region: (iv){(x,y):x^2+...

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  16. (i) Find the area of the region given by: {(x,y):x^2leyle|x|}.

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  17. Find the area bounded by curves {(x,y): ygex^2 and y = |x|}

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  18. (iii) Find the area of the region bounded by the parabola y=x^2 and y=...

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  19. Using integration, find the area of the region bounded by the followin...

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  20. Using integration, find the area of the region bounded by the followin...

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