The value of I=∫011-x1+xdx is
π2+1
π2-1
-1
1
The explanation for the correct answer.
Solve for the value of the given integral.
I=∫011-x1+xdx
Let, x=cos2θdx=-2sin2θdθ
I=∫π401-cos2θ1+cos2θ-2sin2θdθ=∫0π4sinθcosθ2sin2θdθ∵cos2θ=cos2θ-sin2θ,cos2θ+sin2θ=1=2∫0π42sin2θdθ∵sin2θ=2sinθcosθ=2∫0π41-cos2θdθ∵cos2θ=cos2θ-sin2θ,cos2θ+sin2θ=1=2θ-sin2θ20π4=2π4-12=π2-1
Hence, option(B) is the correct answer.