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  • Find the area of the region bounded by x^2 = 4y, y = 2, y = 4 and the y-axis in the first quadrant.

Q : 3       Find the area of the region bounded by  x^2=4y,y=2,y=4  and the y-axis in the first quadrant.
 

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The area bounded by the curves  x^2=4y,y=2,y=4  and the y-axis in the first  quadrant is ABCD.

 

= \int^4_{2} x dy

= \int^4_{2} 2\sqrt{y} dy

= 2\int^4_{2} \sqrt{y} dy

=2\left \{ \frac{y^{\frac{3}{2}}}{\frac{3}{2}} \right \}^4_{2}

= \frac{4}{3}\left \{ (4)^{\frac{3}{2}}-(2)^{\frac{3}{2}} \right \}

= \frac{4}{3} \left \{ 8 -2\sqrt 2 \right \}

= \left \{ \frac{32-8\sqrt 2}{3} \right \}\ units.

Posted by

Divya Prakash Singh

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