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Chapter 4: Q. 39 (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�1x+5dx

Short Answer

Expert verified

Ans: The exact value is,鈭�鈭�32鈥�1x+5dx=ln(7)-ln(2)

Step by step solution

01

Step 1. Given information.

given,

鈭�鈭�32鈥�1x+5dx

02

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

The exact value is calculated as shown below,

Substitute u=x+5

鈭�鈭�32鈥�1x+5dx=鈭�鈭�32鈥�1udx=ln(u)鈭�32=ln(x+5)鈭�32=ln(7)-ln(2)

Therefore, the exact value is,ln(7)-ln(2).

03

Step 3. Check: 

The required graph is,

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