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Find the area bounded by the curve y=x(...

Find the area bounded by the curve `y=x(x-1)(x-2)` and the x-axis.

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To find the area bounded by the curve \( y = x(x-1)(x-2) \) and the x-axis, we will follow these steps: ### Step 1: Rewrite the function First, we expand the function: \[ y = x(x-1)(x-2) = x(x^2 - 3x + 2) = x^3 - 3x^2 + 2x \] ...
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NAGEEN PRAKASHAN ENGLISH-APPLICATIONS OF INTEGRALS-Miscellaneous Exercise
  1. Find the area bounded by the curve y=x(x-1)(x-2) and the x-axis.

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

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  3. Find the area between the curves y = xand y=x^2.

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  4. Find the area of the region lying in the first quadrant and bounded b...

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  5. Sketch the graph y=|x+3|dot Evaluate int(-6)^0|x+3|dxdot What does the...

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  6. Find the area between the x-axis and the curve y=sinx from x=0 to x=2p...

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  7. Find the area of the region enclosed by the parabola y^2=4a x\ a n d t...

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  8. Find the area enclosed by the parabola 4y=3x^2 and the line 2y=3x+12.

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  9. Find the area of the smaller region bounded by the ellipse (x^2)/9+(y^...

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

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  11. Find the area of the region enclosed by the parabola x^2=y , the li...

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  12. Using the method of integration find the area bounded by the curve ...

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

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

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  15. Using the method of integration find the area of the region bounded b...

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  16. Find the area of the region {(x , y): y^2lt=4x ,4x^2+4y^2lt=9}

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  17. Area bounded by the curve y=x^3, the x-axis and the ordinates x = -2 ...

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  18. The area bounded by the curve y=x |x|, x-axis and the ordinates x=-1 &...

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  19. The area of the circle x^2+y^2=16exterior to the parabola y^2=6xis(A) ...

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

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