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The given equations are

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

...(1)
(In the first quadrant)
and y = 0 ...(2)
[∴ x-axis has equation y = 0]
From (1) and (2), we get,

0 space equals space 2 square root of 1 minus straight x squared end root space space space space space space space space rightwards double arrow space space space space space square root of 1 minus straight x squared end root space equals space 0

rightwards double arrow space space space 1 minus straight x squared space equals space 0 space space space space space space space space space space space space rightwards double arrow space space straight x squared space equals space 1 space space space space space space space space rightwards double arrow space space space space straight x space equals space minus 1 comma space space 1

Required area OAB =

integral subscript 0 superscript 1 straight y space dx space equals space 2 integral subscript 0 superscript 1 square root of 1 minus straight x squared space end root space dx

equals space 2 space open square brackets fraction numerator straight x square root of 1 minus straight x squared end root over denominator 2 end fraction plus 1 half sin to the power of negative 1 end exponent straight x close square brackets subscript 0 superscript 1 equals space open square brackets straight x square root of 1 minus straight x squared end root plus sin to the power of negative 1 end exponent straight x close square brackets subscript 0 superscript 1 equals left parenthesis 0 plus sin to the power of negative 1 end exponent 1 right parenthesis space minus space left parenthesis 0 plus sin to the power of negative 1 end exponent 0 right parenthesis space equals space 0 plus straight pi over 2 minus left parenthesis 0 plus 0 right parenthesis space equals space straight pi over 2

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

824 Views

13.

Give the rough sketch of the curve y² = x and the line x = 4 and find the area between the curve and the line.

150 Views

14.

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

183 Views

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.

741 Views

16.

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

220 Views

17.

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

341 Views

18.

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

287 Views

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.

136 Views

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.

151 Views