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Find by integration the area of the regi...

Find by integration the area of the region bounded by the curve `y=2x-x^2` and the x-axis.

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`y=4x-x^(2) " " ` …(1)
Equation of X-axis `y=0 " " ` …(2)
Their points of intersection are O(0, 0) and A(4, 0).
Now draw the graph of the curve and shade the common region.

Required area `=int _(0)^(4)ydx`
`=int_(0)^(4)(4x-x^(2))dx`
`=[2x^(2)-(x^(3))/(3)]_(0)^(4)`
`=32-(64)/(3)=(32)/(3)sq.` units.
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NAGEEN PRAKASHAN-APPLICATIONS OF INTEGRALS-Miscellaneous Exercise
  1. Find by integration the area of the region bounded by the curve y=2x-x...

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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 of y = |x + 3|and evaluateint-6 0|x+3|dx.

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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 enclosed between the parabola y^2=4a xand the line y = ...

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  8. Find the area enclosed by the parabola 4y=3x^2 and the line2y = 3x + ...

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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. The area (in square units) bounded by the curve y=x^3, the x-axis and ...

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

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  19. The area of the circle x^2+y^2=16 exterior to the parabola y^2=6x is

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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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