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Find the area of the region {(x ,y): y^...

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

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Given curves are` y^2=4x ` ....(1)
`4x^2+4y^2=9`
...(2) ⇒`x^2+y^2=9/4`
​ Center of circle is (0,0) and radius of circle is 3/2
Putting the value from equation (1) in equation (2),
`4x^2+16x−9=0`
⇒`x=1/2​,−9/2​`
...
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NCERT-APPLICATION OF INTEGRALS-MISCELLANEOUS EXERCISE
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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 bounded by the curve y = sin x between x = 0 and x=2pi.

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  4. Using the method of integration find the area of the triangle ABC, co...

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

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

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

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

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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. Sketch the graph of y = |x + 3|and evaluateint-6 ^0|x+3|dx.

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

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

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

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  15. the area between the curves y= x^2 and y =4x is

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

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  17. Find the area of the region enclosed by the parabola x^(2)=y and the l...

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

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  19. The area bounded by the y-axis, y = cos xand y = s in xwhen 0lt=xlt=p...

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