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Chapter 4: Q. 32 (page 404)

Integral Formulas:

Fill in the blanks to complete each of the following integration formulas.

(The last six formulas involve hyperbolic functions and their inverses.)

鈭�1xdx=______.

Short Answer

Expert verified

Ans:鈭�1xdx=ln(x)+c

Step by step solution

01

Step 1. Given information:

鈭�1xdx

02

Step 2. Solution:

鈭�1xdx=鈭�x-1dx=ln(x)+c

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Most popular questions from this chapter

Use the Fundamental Theorem of Calculus to find the exact values of the given definite integrals. Use a graph to check your answer.

鈭�0蟺鈥�sin2鈦�x+cos2鈦�xdx

Find the sum or quantity without completely expanding or calculating any sums.

Given 鈭�k=14ak=7and,鈭�k=04bk=10,a0=2. Find the value of鈭�k=042ak+3bk.

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.

鈭�613(1-2x)2+4xdx

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.

鈭�06(3x+2)dx

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.

limn鈫�鈭�鈭�k=1nk2+k+1n
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