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Chapter 4: Q. 19 (page 403)

Fill in the blanks to complete each sum formula:

鈭�k=1nk3=

Short Answer

Expert verified

The complete sum formula is鈭�k=1nk3=n2(n+1)24路

Step by step solution

01

Step 1. Given information.

Given incomplete sum formula is following.

鈭�k=1nk3=

02

Step 2. Explanation.

If n is a positive integer, then by the induction method sigma notation for k3will be following.

鈭�k=1nk3=n2(n+1)24

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Most popular questions from this chapter

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. (Hint for Exercise 54: tanx=sinxcosx).

鈭�e3x-2e4xe2xdx.

Approximate the same area as earlier but this time with eight rectangles is this over approximation or under approximation of the exact area under the graph

Verify that鈭�cotxdx=ln(sinx)+C. (Do not try to solve the integral from scratch.)

Describe an example that illustrates that 鈭�ab|f(x)|dx is not equal to |鈭�abf(x)dx|.

Repeat Exercise 13 for the function f shown above at the right, on the interval [-2,2]
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