Question
The line y=m x bisects the area unclosed by lines x=0, y=0 and x= 3 2 and the curve y=1+4 x-x^2. Then, the value of m is
BITSAT
Mathematics
Area Under Curves
2024
BITSAT 2024 (Memory Based Paper 3)
BITSAT Mathematics Question (2024) — Solution
Options
- A. 13 6
- B. 13 2
- C. 13 5
- D. 13 7
Answer
A. 13 6
Step-by-step solution
Given, y=1+4 x-x^2 aligned & d y d x =4-2 x=0 x=2 [point of maxima] \\ & y_ =1+4 2-4=5 aligned when, x=0, y=1 Graph according to question and above information aligned & If y=m x bisects the area bounded \\ & A_1=A_2 \\ & _0^ 3 / 2 (1+4 x-x^2 ) d x=2 _0^ 3 / 2 m x d x \\ & [x+2 x^2- x^3 3 ]_0^ 3 / 2 = [m x^2 ]_0^ 3 / 2 \\ & 3 2 +2 9 4 - 27 8 1 3 =m 9 4 \\ & m= 13 6 aligned
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