The line y=mx bisects the area enclosed by the curve y=1+4x−x2 and the lines x=0, x=32 and y=0 . Then the value of m is:

2⋅12(32⋅3m2)=∫03/2(1+4x−x2)dx9m4=x+2x2−x33]03/2=32+92−278⋅13=6−98=398m=136

The line y=mx bisects the area enclosed by the curve y=1+4x−x2 and the lines x=0, x=32 and y=0 . Then the value of m is:

2⋅12(32⋅3m2)=∫03/2(1+4x−x2)dx9m4=x+2x2−x33]03/2=32+92−278⋅13=6−98=398m=136

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The line $y = m x$ bisects the area enclosed by the curve $y = 1 + 4 x - x^{2}$ and the lines $x = 0$ , $x = \frac{3}{2}$ and $y = 0$ . Then the value of $m$ is:

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$\frac{13}{6}$

$\frac{6}{13}$

$\frac{3}{2}$

answer is A.

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$2 \cdot \frac{1}{2} (\frac{3}{2} \cdot \frac{3 m}{2}) = \int_{0}^{3 / 2} (1 + 4 x - x^{2}) d x$

${\frac{9 m}{4} = x + 2 x^{2} - \frac{x^{3}}{3}]}_{0}^{3 / 2} = \frac{3}{2} + \frac{9}{2} - \frac{27}{8} \cdot \frac{1}{3} = 6 - \frac{9}{8} = \frac{39}{8}$

$m = \frac{13}{6}$

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The line y=mx bisects the area enclosed by the curve y=1+4x−x2 and the lines x=0, x=32 and y=0 . Then the value of m is:

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The line $y = m x$ bisects the area enclosed by the curve $y = 1 + 4 x - x^{2}$ and the lines $x = 0$ , $x = \frac{3}{2}$ and $y = 0$ . Then the value of $m$ is: