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Chapter 4: Q. 43 (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�14鈥�2x+3x2+3x+4dx

Short Answer

Expert verified

Ans: The exact value of,鈭�14鈥�2x+3x2+3x+4dx=ln(32)-ln(8)

Step by step solution

01

Step 1. Given information.

given,

鈭�14鈥�2x+3x2+3x+4dx

02

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

The exact value is calculated as shown below,

鈭�14鈥�2x+3x2+3x+4dx=鈭�14鈥�1udu=[ln鈦�(|u|)]14=ln鈦�42+3(4)+4鈭�ln鈦�(1)2+3(1)+4=ln鈦�(16+12+4)鈭�ln鈦�(1+3+4)=ln鈦�(32)鈭�ln鈦�(8)

Therefore, the exact value is ln鈦�(32)鈭�ln鈦�(8)

03

Step 3. Check:

The required graph is,

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