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

Vector Algebra

Question

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

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Solution

The equation of curve is y² = 4 x
Required area =

integral subscript 1 superscript 4 straight y space dx

equals space integral subscript 1 superscript 4 2 square root of straight x space dx space equals space 2 integral subscript 1 superscript 4 straight x to the power of 1 half end exponent dx equals space 2 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 space 4 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 4 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 4 over 3 left parenthesis 8 minus 1 right parenthesis space equals space 4 over 3 cross times 7 space equals space 28 over 3 space sq. space units

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