Find the area of the region lying in the first quadrant and bounded by x 2 = y - 3, y = 4, y = 6 and the y-axis in the first quadrant. - Wired Faculty

Vector Algebra

Question

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Find the area of the region lying in the first quadrant and bounded by x² = y - 3, y = 4, y = 6 and the y-axis in the first quadrant.

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Solution

The equation of curve is x² = y - 3. which is an upward parabola whose vertex is (0,3).
Lines are y = 4, y = 6
Required area = Area ABCD

equals space integral subscript 4 superscript 6 straight x space dy space equals space integral subscript 4 superscript 6 square root of straight y minus 3 end root space dy

equals space integral subscript 4 superscript 6 left parenthesis straight y minus 3 right parenthesis to the power of 1 half end exponent dy space equals space open square brackets fraction numerator left parenthesis straight y minus 3 right parenthesis 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 4 superscript 6 equals space 2 over 3 open square brackets left parenthesis straight y minus 3 right parenthesis to the power of 3 over 2 end exponent close square brackets subscript 4 superscript 6 space equals space 2 over 3 open square brackets left parenthesis 3 right parenthesis to the power of 3 over 2 end exponent minus left parenthesis 1 right parenthesis to the power of 3 over 2 end exponent close square brackets space equals 2 over 3 left parenthesis 3 square root of 3 space minus space 1 right parenthesis space sq. space units.

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Vector Algebra

Find the area of the region lying in the first quadrant and bounded by x² = y - 3, y = 4, y = 6 and the y-axis in the first quadrant.

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For Daily Free Study Material Join wiredfaculty

Vector Algebra

Find the area of the region lying in the first quadrant and bounded by x2 = y - 3, y = 4, y = 6 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 lying in the first quadrant and bounded by x² = y - 3, y = 4, y = 6 and the y-axis in the first quadrant.