Math  /  Calculus

QuestionSet up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified li y=sin(x),y=0,0xπ;y=\sin (x), \quad y=0, \quad 0 \leq x \leq \pi ; \quad about y=4y=-4 \square dx\int d x Need Help? Read It

Studdy Solution
The volume V V of the solid is given by the integral:
V=π0π[(4+sin(x))2(4)2]dxV = \pi \int_{0}^{\pi} \left[ (4 + \sin(x))^2 - (4)^2 \right] \, dx
The integral expression for the volume is:
π0π[(4+sin(x))216]dx\pi \int_{0}^{\pi} \left[ (4 + \sin(x))^2 - 16 \right] \, dx

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