Sponsor Area

Vector Algebra

Question
CBSEENMA12032693

Find the area bounded by the curve y2 = 4 a (x-1) and the lines x = 1 and y = 4 a.

Solution
The equation of parabola is y2 = 4 a (x-1)    ...(1)
When y = 4 a , from (1) 16 a2 = 4 a (x-1)
⇒ x - 1 = 4 a ⇒ x = 4 a + 1
therefore space space required space area space equals space integral subscript straight x space equals space 1 end subscript superscript straight x equals 4 straight a plus 1 end superscript straight y space dx space equals space integral subscript straight x equals 1 end subscript superscript straight x space equals space 4 straight a plus 1 end superscript 2 square root of straight a space square root of straight x minus 1 end root space dx open square brackets because space of space left parenthesis 1 right parenthesis close square brackets
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