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Chapter 4: Q. 34 (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.

∫24 14−3xdx

Short Answer

Expert verified

Ans: The exact value of,∫24 14−3xdx=−13(ln⁡8)+13(ln⁡2)

Step by step solution

01

Step 1. Given information.

given,

∫24 14−3xdx

02

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

The exact value is calculated as shown below,

∫24 14−3xdx=−13[ln⁡(|4−3x|)]24=−13[ln⁡(|4−3(4)|)−ln⁡(|4−3(2)|)]=−13[ln⁡(8)−ln⁡(2)]=−13(ln⁡8)+13(ln⁡2)

Therefore, the exact value islocalid="1648629053226" −13(ln⁡8)+13(ln⁡2)

03

Step 3. Check 

The required graph is,

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