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Find the area lying above the x-axis and...

Find the area lying above the x-axis and under the parabola `y=4x-x^2`

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To find the area lying above the x-axis and under the parabola given by the equation \( y = 4x - x^2 \), we can follow these steps: ### Step 1: Find the points where the parabola intersects the x-axis To find the points of intersection with the x-axis, we set \( y = 0 \): \[ 4x - x^2 = 0 \] ...
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RD SHARMA-APPLICATION OF INTEGRALS-Solved Examples And Exercises
  1. Find the area of the region bounded by the line y=3x+2, the x-axis and...

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  2. Using the method of integration find the area bounded by the curve |x|...

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  3. Find the area lying above the x-axis and under the parabola y=4x-x^2

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  4. Draw a rough sketch to indicate the region bounded between the curve y...

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  5. Make a rough sketch of the graph of the function y=4-x^2,\ 0lt=xlt=2 a...

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  6. Using integration, find the area bounded by the lines x+2y=2, y−x=1 an...

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  7. Find the area under the curve y=sqrt(6x+4)(above the x-axis) from x=0 ...

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

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  9. Draw a rough sketch of the graph of the curve x^2/4+y^2/9=1 and evalua...

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  10. Using integration, find the area of the region bounded by the line 2y ...

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  11. Sketch the graph of y=|x-5|. Evaluate int0^1 |x-5|dx. What does this v...

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  12. Sketch the graph of y=|x+3|. Evaluate int-6^0 |x+3|dx. What does the v...

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  13. The area of the region bounded by the curve xy-3-2y- 10=0, X-axis and ...

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  14. Draw a rough sketch of the curve y=x/pi + 2 sin^2 x, and find the area...

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  15. Draw a rough sketch of the curve y=x/pi + 2 sin^2 x, and find the area...

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  16. Find the area bounded by the curve y=cos x ,\ x-axis and the ordinate...

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  17. Find the area bounded by the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1and th...

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  18. Examples: Find the area of the region bounded by the curve y^2 = 2y - ...

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  19. Find the area bounded by the curve y^2=4a x and the lines y=2\ a n d\ ...

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

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