6.3 Volume by slicing 6.4 Volume by shells 6.5 Length of curves 6.6 Surface area 6.7 Physical applications 6.8 Logarithmic and exponential functions revisited 6.9 Exponential models 6.10 Hyperbolic functions 7. Integration Techniques 7.1 Basic approaches ...
Volume by Slicing Arc Length Surface Area of a Surface of Revolution Differential Equations Centroids Work Hydrostatic Force Applications of Differentiation Tangent and Normal Lines Newton's Method Taylor Polynomials Differentials and the Linear Approximation ...
Slicing MethodLearning Outcomes Determine the volume of a solid by integrating a cross-section (the slicing method)Volume and the Slicing MethodJust as area is the numerical measure of a two-dimensional region, volume is the numerical measure of a three-dimensional solid. Most of us have ...
Volume of a Solid of Revolution: Rotation about x = 2 Work Conical Tank Numeric Integration: Trapezoid Rule Trig Substitution Sequence of Constants Trig Substitution Partial Sums for a Series of Constants Integration by Partial Fractions Volume by Slicing ...
We can confirm that our results make sense by observing a graph of the equation. Notice that the graph crosses the axes where we predicted it would.How To: Given an equation, find the intercepts Find the x-intercept by setting y=0y=0 and solving for xx. Find the y-intercept by ...
Volume of a Solid of Revolution: Rotation about x = 2 Work Conical Tank Numeric Integration: Trapezoid Rule Trig Substitution Sequence of Constants Trig Substitution Partial Sums for a Series of Constants Integration by Partial Fractions Volume by Slicing ...
Area under a curve Area between curves Volume by slicing, disks and washers Volume by cylinders Volume of solids with known cross sections Motion along a line revisited Differential Equations Slope fields Introduction Separable Exponential growth and decay...
So, by the shell method, the volume is It can be verified that the shell method gives the same answer as slicing. FI GURE 7 y x 2 [ 1 2 x 4 1 5 x 5 ] 0 2 2 (8 32 5 ) 16 5 V y 2 0 2 x 2x 2 x 3 dx 2 y 2 0 2x 3 x 4 dx f x 2x 2 x 3 2 x y ...
Our textbook (along with the world of math) has adopted the rule of four. Just like Pre Calculus we will be exploring Calculus graphically, numerically, algebraically, and verbally. We will find the connections between graphs (with out equations) and data and how it relates to a graph. ...
Applications of Integration Area under a curve Area between curves Volume by slicing, disks and washers Volume by cylinders Volume of solids with known cross sections Motion along a line revisited Differential Equations Slope fields Introduction Separable Exponential growth and decay About...