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Chapter 4: Q. 59 (page 327)
Given a simple proof that
We have proved
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Prove that in three different ways:
(a) algebraically, by calculating a limit of Riemann sums;
(b) geometrically, by recognizing the region in question as a trapezoid and calculating its area;
(c) with formulas, by using properties and formulas of definite integrals.
If , and , then find the values of each definite integral in Exercises . If there is not enough information, explain why.
Show thatis an anti-derivative of
Without using absolute values, how many definite integrals would we need in order to calculate the absolute area between f(x) = sin x and the x-axis on ?
Will the absolute area be positive or negative, and why? Will the signed area will be positive or negative, and why?
Determine which of the limit of sums in Exercises 47鈥�52 are infinite and which are finite. For each limit of sums that is finite, compute its value
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