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Find the area bounded by the curve y=(4-...

Find the area bounded by the curve `y=(4-x^2)` the y-axis and the lines y=0 y=3

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To find the area bounded by the curve \( y = 4 - x^2 \), the y-axis, and the lines \( y = 0 \) and \( y = 3 \), we can follow these steps: ### Step 1: Understand the curve and the boundaries The curve \( y = 4 - x^2 \) is a downward-opening parabola. We need to find the area between this curve and the y-axis, from \( y = 0 \) to \( y = 3 \). ### Step 2: Find the points of intersection To find the points where the curve intersects the line \( y = 3 \): \[ ...
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RS AGGARWAL-AREA OF BOUNDED REGIONS -Exercise 17
  1. Evaluate the area bounded by the ellipse (x^2)/(4)+(y^2)/(9)=1 above...

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  2. Using integration, find the area of the region bounded by the lines Y ...

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  3. Find the area bounded by the curve y=(4-x^2) the y-axis and the lines ...

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  4. Using integration, find the area of the region bounded by the triangle...

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  5. Using integration, find the area of the region bounded by the lines...

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  6. Using intergration find the are of the region bounded between the lin...

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  7. Using integration, find the area of the region bounded by the line y-1...

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  8. Sketch the region lying in the first quadrant and bounded by y = 4x^2 ...

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  9. Sketch the region lying in the first quadrant and bounded by y=9x^2...

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  10. Find the area of the region enclosed between the two circles x^2 + y^2...

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  11. Sketch the region common to the circle x^2 +y^2=16 and the parabola x...

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  12. Sketch the region common to the cirvle x^2+y^2=25 and the parabola y^...

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  13. Draw a rough sketch of the region {(x,y): y^2 le 3x,3x^2 + 3y^2 le16 }...

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  14. Draw a rough sketch and find the area of the region bounded by the par...

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  15. Find by intergraiton the area bounded by the curve y^2 = 4ax and the l...

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

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  17. Find the area bounded by the curve y=cos x between x=0 and x=2pi

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  18. Compare the areas under the curves y=cos ^2 x and y= sin ^2x between x...

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  19. Using integration find the area of the triangular region whose side...

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  20. Find the area of the region {(x,y) : x^2 le y le x }

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