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Chapter 5: Q. 8 (page 441)

Verify that x2-1+x2x4+3x2+4is a valid result for the polynomial long-division calculation performed to divide the polynomial x6+2x4+2x2-4by the polynomialx4+3x2+4

Short Answer

Expert verified

The given resultx2-1+x2x4+3x2+4is verified.

Step by step solution

01

Step 1. Given Information

The given improper function isx6+2x4+2x2-4x4+3x2+4

02

Step 2. Calculation

The long division methof is shown below,

So, the improper function is written as a sum of an integer and a proper function below,

x6+2x4+2x2-4x4+3x2+4=x2-1+x2x4+3x2+4

Thus, the result is verified.

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Most popular questions from this chapter

For each function u(x) in Exercises 9鈥�12, write the differential du in terms of the differential dx.

u(x)=1x

Explain why 鈭�2xx2+1dxand 鈭�1xlnxdxare essentially the same integral after a change of variables.

True/False: Determine whether each of the statements that follow is true or false. If a statement is true, explain why. If a statement is false, provide a counterexample.

(a) True or False: The substitution x = 2 sec u is a suitable choice for solving鈭�1x2鈭�4dx.

(b) True or False: The substitution x = 2 sec u is a suitable choice for solving鈭�1x2鈭�4dx.

(c) True or False: The substitution x = 2 tan u is a suitable choice for solving鈭�1x2+4dx.

(d) True or False: The substitution x = 2 sin u is a suitable choice for solving鈭�x2+4鈭�5/2dx

(e) True or False: Trigonometric substitution is a useful strategy for solving any integral that involves an expression of the form x2鈭�a2.

(f) True or False: Trigonometric substitution doesn鈥檛 solve an integral; rather, it helps you rewrite integrals as ones that are easier to solve by other methods.

(g) True or False: When using trigonometric substitution with x=asinu, we must consider the cases x>a and x<-a separately.

(h) True or False: When using trigonometric substitution with x=asecu, we must consider the cases x>a and x<-a separately.

Solve the integral

鈭�3-xx-1dx

Solve the integral

鈭�1x2x2-9dx
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