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QJEEM21Ma1075: JEE Main 2021 Mathematics - Class 12 JEEM21Ma1075 Solution: If the line y = mx bisects the area enclosed by the lines x =…

If the line y = mx bisects the area enclosed by the lines x = 0, y = 0, x = 32{3 \over 2} and the curve y = 1 + 4x −- x2, then 12 m is equal to _____________.

Step-by-Step Verified Solution

JEE Main 2021 (Online) 31st August Evening Shift Mathematics - Area Under The Curves Question 81 English Explanation

According to the question,

12∫03/2(1+4x−x2)dx=∫03/2mx dx{1 \over 2}\int_0^{3/2} {(1 + 4x - {x^2})dx = \int_0^{3/2} {mx\,dx} }

⇒12[(x+2x2−x33)]03/2=m2[x]03/2⇒32+92−98=9m4\Rightarrow {1 \over 2}\left[ {\left( {x + 2{x^2} - {{{x^3}} \over 3}} \right)} \right]_0^{3/2} = {m \over 2}[x]_0^{3/2} \Rightarrow {3 \over 2} + {9 \over 2} - {9 \over 8} = {{9m} \over 4}

⇒\Rightarrow m = 39/18 ⇒\Rightarrow 12m = 26

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