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Chapter 4: Q. 78 (page 387)
Prove that for the region between the graph of a function f and the x-axis on an interval [a, b], the absolute area is always greater than or equal to the signed area.
Hence, proved.
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If and ,then find the values of each definite integral in Exercises . If there is not enough information, explain why.
.
Sum and constant-multiple rules: State the sum and constant-multiple rules for (a) derivatives and (b) limits.
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?
Write out all the integration formulas and rules that we know at this point.
Use integration formulas to solve each integral in Exercises 21–62. You may have to use algebra, educated guess and-check, and/or recognize an integrand as the result of a product, quotient, or chain rule calculation. Check each of your answers by differentiating.
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