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Chapter 4: Q. 37 (page 373)

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

鈭�鈭�11鈥�2x4xdx

Short Answer

Expert verified

Ans: The exact value of,鈭�鈭�11鈥�2x4xdx=32ln(2).

Step by step solution

01

Step 1. Given information.

given,

鈭�鈭�11鈥�2x4xdx

02

Step 2. The objective is to determine the exact value of the definite integral.  

The exact value is calculated as shown below,

鈭�鈭�11鈥�2x4xdx=鈭�鈭�11鈥�2x4鈭�xdx=鈭�鈭�11鈥�2x2鈭�2xdx=鈭�鈭�11鈥�2鈭�xdx=鈭�1ln鈦�(2)2鈭�x鈭�11=鈭�12xln鈦�(2)鈭�11=鈭�121ln鈦�(2)+12鈭�1ln鈦�(2)=32ln鈦�(2)

Therefore, the value is32ln鈦�(2).

03

Step 3. Check

The required graph is,

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Most popular questions from this chapter

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�04(2x-3)2+5dx

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

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�(tanx+xsec2x)dx.

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