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Chapter 4: Q. 39 (page 340)
In Exercises 39鈥�44, write out the sigma notation for the Riemann sum described in such a way that the only letter which appears in the general term of the sum is k. Don鈥檛 calculate the value of the sum; just write it down in sigma notation.
The right sum is given by
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Calculate the exact value of each definite integral in Exercises 47鈥�52 by using properties of definite integrals and the formulas in Theorem 4.13.
Use the Fundamental Theorem of Calculus to find the exact values of the given definite integrals. Use a graph to check your answer.
Use integration formulas to solve each integral in Exercises 21鈥�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.
Prove part (b) of theorem 4.4 in the case when n is even: if n is a positive even integer, then
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?
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