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Chapter 4: Q. 41 (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�2xx2+5dx

Short Answer

Expert verified

Ans: The exact value is,鈭�鈭�32鈥�2xx2+5dx=ln鈦�(9)鈭�ln鈦�(14)

Step by step solution

01

Step 1. given information.

given,

鈭�鈭�32鈥�2xx2+5dx

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�2xx2+5dx=2鈭�鈭�32鈥�xx2+5dx=2鈭�12uduu=1+x2,du=2xdx=212鈭�1udu=[ln鈦�(|u|)]鈭�32=ln鈦�5+x2鈭�32=ln鈦�5+22鈭�ln鈦�5+(鈭�3)2=ln鈦�(9)鈭�ln鈦�(14)

Therefore, the exact value is,localid="1648640074319" ln鈦�(9)鈭�ln鈦�(14)

03

Step 3. Check

The required graph is,

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