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Vector Algebra

Question
CBSEENMA12032699
Wired Faculty App

Find the area of the region bounded by the curve  y = x2 and the line y = 4.

Solution

The equation of parabola is
y = x2    ...(1)
The equation of line is
                y = 4
This parabola is symmetrical about y-axis
therefore space space space requird space area space POQRP space equals space 2 space left parenthesis area space OQRO right parenthesis
                                           equals space 2 space integral subscript 0 superscript 4 straight x space dy space equals space 2 space integral subscript 0 superscript 4 square root of straight y space dy equals space 2 integral subscript 0 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 0 superscript 4 space equals space 4 over 3 open square brackets straight y to the power of 3 over 2 end exponent close square brackets subscript 0 superscript 4 space equals space 4 over 3 open square brackets 4 to the power of 3 over 2 end exponent minus 0 close square brackets space equals space 4 over 3 open square brackets left parenthesis 2 squared right parenthesis to the power of 3 over 2 end exponent minus 0 close square brackets space equals space 4 over 3 cross times 2 cubed space equals space 4 over 3 cross times 8 space equals space 32 over 3 space sq. space units

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