If _0^1 (1-x)/(1+x) dx = A 2 + B, then the value of A and B are Option 1: A=2, B=2 Option 2: A=2, B=1 Option 3: A=2, B=-1 Option 4: A=1, B=2

Answer: A=2, B=-1. Solution: Write (1-x)/(1+x)=2/(1+x)-1. Then _0^1(2/(1+x)-1)dx=[2(1+x)-x]_0^1=2 2-1. Comparing, A=2 and B=-1.

Calculus

Integrals

Easy

common

If $\int_0^1 \frac{1-x}{1+x} dx = A\log 2 + B$ , then the value of A and B are

$A=2, B=2$

$A=2, B=1$

$A=2, B=-1$

$A=1, B=2$

✅ Correct Option: 3

Write $\frac{1-x}{1+x}=\frac{2}{1+x}-1$ .

Then $\int_0^1\left(\frac{2}{1+x}-1\right)dx=\left[2\log(1+x)-x\right]_0^1=2\log 2-1$ .

Comparing, $A=2$ and $B=-1$ .

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