By Mark Zegarelli
An easy-to-understand primer on complicated calculus topicsCalculus II is a prerequisite for plenty of well known university majors, together with pre-med, engineering, and physics. Calculus II For Dummies bargains professional guideline, suggestion, and tips on how to support moment semester calculus scholars get a deal with at the topic and ace their tests. It covers intermediate calculus issues in undeniable English, that includes in-depth assurance of integration, together with substitution, integration suggestions and while to take advantage of them, approximate integration, and unsuitable integrals. This hands-on advisor additionally covers sequences and sequence, with introductions to multivariable calculus, differential equations, and numerical research. better of all, it comprises sensible workouts designed to simplify and increase figuring out of this complicated topic.
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Additional resources for Calculus II For Dummies (For Dummies (Math & Science))
But, even a lousy approximation is better than none at all. To get a better approximation, try cutting the figure that you’re measuring into a few more slices, as shown in Figure 1-11. y y = x2 Figure 1-11: A closer approximation; the area is approximated by four rectangles. x x=1 x=5 Again, this approximation is going to be less than the actual area that you’re seeking. This time, each rectangle has a width of 1. And the tops of the four rectangles cut across where the function x2 meets x = 1, x = 2, x = 3, and x = 4, so their heights are 1, 4, 9, and 16, respectively.
Polynomials enjoy a special status in math because they’re particularly easy to work with. For example, you can find the value of f(x) for any x value by plugging this value into the polynomial. Furthermore, polynomials are also easy to differentiate and integrate. Knowing how to recognize polynomials when you see them will make your life in any math course a whole lot easier. Powering through powers (exponents) Remember when you found out that any number (except 0) raised to the power of 0 equals 1?
1 1 x 1 1 x –1 1 x –1 You can still use the trusty old methods of classical geometry to find the areas of these figures. But analytic geometry opens up more possibilities — and more problems. Discovering a new area of study Figure 1-3 illustrates three curves that are much easier to study with analytic geometry than with classical geometry: a parabola, an ellipse, and a hyperbola. 13 14 Part I: Introduction to Integration y y 2 1 x2 = y y2 =1 4 1 y = 1 1 x y = x2 Figure 1-3: A parabola, an ellipse, and a hyperbola embedded on the graph.