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Chapter 4: Q. 36 (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�01鈥�x1+x2dx

Short Answer

Expert verified

Ans: The exact value of,鈭�01鈥�x1+x2dx=12ln|2|.

Step by step solution

01

Step 1. Given information.

given,

鈭�01鈥�x1+x2dx

02

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

Let,

u=1+x2du=2xdx

The exact value is calculated as shown below,

鈭�01鈥�x1+x2dx=鈭�01鈥�12udu=12鈭�01鈥�1udu=12[ln鈦�(|u|)]01=12ln鈦�1+12鈭�ln鈦�1+02=12(ln鈦�|2|鈭�ln鈦�|1|)=12ln鈦�|2|

Therefore, the exact value is12ln|2|.

03

Step 3. Check 

The required graph is,

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