Calculate the surface area Integral of object obtained by rotating the function x=2y+5 for x=-1 and -2 about y axis
If the curve "x=x(y)" is rotated around "y"-axis, the formula for the surface area is: "S=2\\pi\\int_{y_1}^{y_2}x(y)\\sqrt{1+(x'(y))^2}dy". In our case we have: "x=2y+5," "y_1=-3," "y_2=-3.5". We get: "S=2\\pi\\int_{-3}^{-3.5}\\sqrt{5}(2y+5)dy=2\\pi\\sqrt{5}(y^2+5y)|_{y=-3}^{y=-3.5}=\\frac32\\pi\\sqrt{5}" . Thus, the answer is: "S=\\frac32\\pi\\sqrt{5}".
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