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11. Find the area of the region bounded by the curve

straight y space equals space 2 square root of 1 minus straight x squared end root

and x-axis. Draw a rough sketch..

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12. Calculate the area bounded by the parabola y² = 4 a x and its latus rectum.

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The equation of parabola is
y² = x ...(1)
The equation of line is x = 4
Also, we know that parabola is symmetric about x-axis

therefore space space space required space area space equals space 2 space left parenthesis area space ORP right parenthesis

equals space 2 integral subscript 0 superscript 4 space straight y space dx space equals space 2 space integral subscript 0 superscript 4 square root of straight x space dx space space space space space space space space space space space space space open square brackets because space of space left parenthesis 1 right parenthesis close square brackets

equals space 2 space integral subscript 0 superscript 4 straight x to the power of 1 half end exponent dx space equals space 2 open square brackets fraction numerator straight x to the power of begin display style 3 over 2 end style end exponent over denominator begin display style 3 over 2 end style end fraction close square brackets subscript 0 superscript 4 space equals space 4 over 3 open square brackets straight x to the power of 3 over 2 end exponent close square brackets subscript 0 superscript 4 space equals space 4 over 3 open square brackets 4 to the power of 3 over 2 end exponent minus 0 close square brackets space equals space 4 over 3 cross times square root of 64 space equals space 4 over 3 cross times 8 space equals space 32 over 3 space sq space. units.

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14.

Find the area bounded between the curve y² = x and the line x = 3. Draw the rough sketch also.

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15. The area between x = y² and x = 4 is divided into two equal parts by the line x = a, find the value of a.

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16.

Find the area of the region bounded by the curve y = x² and the line y = 4.

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17.

Find the area of the region bounded by the curve y² = 4x and the line x = 3.

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18.

Using definite integrals, find the area of the circle x² + y² = a².

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19. Find the area of the region bounded by the ellipse

straight x squared over 9 plus straight y squared over 4 space equals space 1.

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20. Find the area of the region bounded by the ellipse

straight x squared over 16 plus straight y squared over 9 space equals 1.

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