Find the area of the region bounded by the curve y 2 = x and the lines x = 1, x = 4 and the x-axis in the first quadrant. - Wired Faculty

Vector Algebra

Question

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Find the area of the region bounded by the curve y²= x and the lines x = 1, x = 4 and the x-axis in the first quadrant.

Solution

The equation of curve is y² = x
Required area = $integral subscript 1 superscript 4 space straight y space dx space equals space integral subscript 1 superscript 4 square root of straight x space end root dx space equals integral subscript 1 superscript 4 straight x to the power of 1 half end exponent dx$
$equals space open square brackets fraction numerator straight x to the power of begin display style 3 over 2 end style end exponent over denominator begin display style 3 over 2 end style end fraction close square brackets subscript 1 superscript 4 space equals 2 over 3 open square brackets straight x to the power of 3 over 2 end exponent close square brackets subscript 1 superscript 4 space equals space 2 over 3 open square brackets open parentheses 4 close parentheses to the power of 3 over 2 end exponent minus 1 close square brackets equals space 2 over 3 left parenthesis 8 minus 1 right parenthesis space equals space 2 over 3 cross times 7 space equals space 14 over 3 sq. space units.$

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Vector Algebra

Find the area of the region bounded by the curve y²= x and the lines x = 1, x = 4 and the x-axis in the first quadrant.

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For Daily Free Study Material Join wiredfaculty

Vector Algebra

Find the area of the region bounded by the curve y2 = x and the lines x = 1, x = 4 and the x-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 the curve y²= x and the lines x = 1, x = 4 and the x-axis in the first quadrant.