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angle antiderivative apply approximation axis calculate centroid chain rule circle circular compute constant continuous function converges critical points curve cylinder decimal places defined definition denote differential equation distance diverges double integral dx dy ellipse evaluate EXAMPLE Find the area Find the volume formula function f(x given gives graph Green's theorem height Hence horizontal hyperbola improper integral initial inverse length limit line integral linear mass maximum mean value theorem method minimum value Newton's method obtain parabola paraboloid parametric partial derivatives partition perpendicular plane polar coordinates polynomial Problem radius rate of change real number rectangle rectangular result revolving Riemann sum Section Show shown in Fig slope solid Solution solve spherical square subintervals substitution Suppose surface area tangent line tank theorem tion triangle variables vector field velocity vertical write x-axis xy-plane y-axis zero