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Engineering

Let $f: \mathbb{R} \to \mathbb{R}$ be defined as $f(x) = e^{-x} \sin x$ . If $F: [0, 1] \to \mathbb{R}$ is a differentiable function such that $F(x) = \int_{0}^{x} f(t) dt$ , then the value of $\int_{0}^{1} (F'(x)+f(x))e^x dx$ lies in the interval

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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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