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Engineering

If $(a, b)$ be the orthocentre of the triangle whose vertices are $(1, 2), (2, 3)$ and $(3, 1)$ , and $I_1 = \int_a^b x\sin(4x-x^2)dx$ , $I_2 = \int_a^b \sin(4x-x^2)dx$ , then $36 \frac{I_1}{I_2}$ is equal to :

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A metal wire of uniform mass density having length L and mass M is bent to form a semicircular arc and a particle of mass m is placed at the centre of the arc. The gravitational force on the particle by the wire is: [Diagram: Semicircular arc with mass m at center]

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