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Chapter 4: Q. 40 (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�32鈥�1(x+5)2dx

Short Answer

Expert verified

Ans: The exact value is,鈭�鈭�32鈥�1(x+5)2dx=514

Step by step solution

01

Step 1. Given information.

given expression,

鈭�鈭�32鈥�1(x+5)2dx

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�32鈥�1(x+5)2dx=鈭�鈭�32鈥�(x+5)鈭�2dx=(x+5)鈭�2+1鈭�2+1鈭�32=(x+5)鈭�1鈭�1鈭�32=鈭�1(x+5)鈭�32=鈭�1(2+5)+1(鈭�3+5)=鈭�17+12=鈭�2+714=514

Therefore, the exact value is 514.514

03

Step 3. Check: 

The required graph is,

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Most popular questions from this chapter

Explain why at this point we don鈥檛 have an integration formula for the functionf(x)=secx whereas we do have an integration formula for f(x)=sinx.

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.

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Fill in each of the blanks:

(a) 鈭�x6dx=+C.

(b) is an antiderivative of role="math" localid="1648619282178" x6.

(c) The derivative of is x6.

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.鈭�x2-3x5-7dx
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