Question

Find the area of the region bounded by x² = 4 y, y = 2, y = 4 and the y-axis in the first quadrant.

Solution

The equation of curve is x² = 4y, which is an upward parabola.
Lines are y = 2 and y = 4
Required area = Area ABCD
$equals space integral subscript 2 superscript 4 straight x space dy space equals space integral subscript 2 superscript 4 2 square root of straight y space dy equals space 2 integral subscript 2 superscript 4 straight y to the power of 1 half end exponent dy space equals space 2 open square brackets fraction numerator straight y to the power of begin display style 3 over 2 end style end exponent over denominator begin display style 3 over 2 end style end fraction close square brackets subscript 2 superscript 4 equals space 4 over 3 open square brackets straight y to the power of 3 over 2 end exponent close square brackets subscript 2 superscript 4 space equals space 4 over 3 open square brackets left parenthesis 4 right parenthesis to the power of 3 over 2 end exponent minus left parenthesis 2 right parenthesis to the power of 3 over 2 end exponent close square brackets equals space 4 over 3 left parenthesis 8 minus 2 square root of 2 right parenthesis space equals space fraction numerator 32 minus 8 square root of 2 over denominator 3 end fraction sq. space units$

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Vector Algebra

Find the area of the region bounded by x² = 4 y, y = 2, y = 4 and the y-axis in the first quadrant.

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Vector Algebra

Find the area of the region bounded by x2 = 4 y, y = 2, y = 4 and the y-axis in the first quadrant.

Some More Questions From Vector Algebra Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Find the area of the region bounded by x² = 4 y, y = 2, y = 4 and the y-axis in the first quadrant.