Find the area of the region bounded by the curve y 2 = 4x and the line x = 3. - Wired Faculty

Vector Algebra

Question

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

Solution

The equation of parabola is
y² = 4 x
The equation of line is
x = 3
Also, we know that parabola is symmetric about x-axis
∴ required area = 2 (area ORPO)

$equals space 2 integral subscript 0 superscript 3 2 square root of straight x space dx space equals space 4 space integral subscript 0 superscript 3 straight x to the power of 1 half end exponent dx equals space 4 open square brackets fraction numerator straight x to the power of begin display style 3 over 2 end style end exponent over denominator begin display style 3 over 2 end style end fraction close square brackets subscript 0 superscript 3 space equals space 8 over 3 open square brackets straight x to the power of 3 over 2 end exponent close square brackets subscript 0 superscript 3 space equals space 8 over 3 open parentheses 3 to the power of 3 over 2 end exponent minus 0 close parentheses space equals space 8 over 3 cross times square root of 27 equals space 8 over 3 cross times 3 square root of 3 space equals space 8 square root of 3 space sq. space units.$

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Vector Algebra

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

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Vector Algebra

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

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 = 4x and the line x = 3.