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Sketch the graph of: f(x)={(|x-2|+2,xle2...

Sketch the graph of: `f(x)={(|x-2|+2,xle2),(x^2-2,x>2):}`. Evaluate `int_0^4f(x)dx`. What does the value of this integral represent on the graph?

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MODERN PUBLICATION-APPLICATIONS OF THE INTEGRALS-EXERCISE
  1. Sketch the graph of: f(x)={(|x-2|+2,xle2),(x^2-2,x>2):}. Evaluate int0...

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  2. Using integration, find the area of the circle x^(2)+y^(2)=4

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  3. Using integration, find the area of the circle x^(2)+y^(2)=4

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  4. Find the area of the region bounded by the curve y^2 = 4x and the lin...

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  5. Using integration, find the area bounded between the parabola x^2=4y a...

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  6. Find the area bounded by the curve y^(2)=2y-x and the Y-axis.

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  7. (i) Find the area bounded by y=2x+3, the x-axis and the ordinates x=-2...

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  8. Find the area bounded by y=x, the x-axis and the lines x=-1 and x=2.

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  9. Find the area of the region bounded by (i) y=x^4, x=1,x=5 and x-axis.

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  10. Find the area of the region bounded by (ii) y=x^2,x=0,x=2 and x-axis.

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  11. Find the area of the region bounded by (iii) y=x^2-4, x=0,x=3 and x-ax...

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  12. Find the area of the region bounded by (iv) y=x^3,x=2,x=4 and x-axis.

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  13. Find the area of the region bounded by y^2 = 9x, x=2, x=4 and the x-a...

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  14. Find the area of the region bounded by y=4x^2,x=0,y=1,y=4 in the first...

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  15. Calculate the area undder the curve : y=2sqrtx between the ordinates x...

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  16. Find the area under the curve y=(x^2+2)^(2)+2x between the ordinates x...

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

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

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

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  20. (ii) Using definite integrals, find the area of the circle (x-1)^2+y^2...

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  21. Determine the area enclosed between the curve y=cos 2x, 0lexlepi/4 and...

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