How do you turn an integral into a double integral?
just by renaming the variable of integration in the second factor. But now, this last can be viewed as an iterated integral, and then as a double integral: (17.73) ? 0 e x2dx ?K
How did Newton and Leibniz develop the concept of definite integrals?
Later on, the concept of the de?nite integral was also developed.Newton and Leibnizrecognized the importance of the fact that ?nding derivatives and ?nding integrals (i.e.,antiderivatives) areinverse processes, thus making possible the rule for evaluating de?niteintegrals.All these matters are systematically introduced in Part II of the book.
What is the philosophy of integration techniques?
The general philosophy is that techniques should give you a tool toconvert unknown integrand to known integrands. Have a good reservoir of known integrals, and Be uent with integration techniques. The rst item is something you accumulate by experience.
What are iterated integrals?
f x y dx =dy These are called the iterated integrals, and provide the technique for evaluating double integrals. For a general region, we try to break it up into a ?nite set of nonoverlapping pieces, each of which is either type 1 or type 2.
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