If the real part of the complex number (1 - cos θ + 2i sin θ)⁻¹ is 1/5 for θ (0,π), then the value of the integral ∫₀^θ sin x dx is equal to:

Integral Calculus: JEE Main 2021 Mathematics question

JEE Main 2021 · 20 Jul, Evening shift · Q3408

JEE Main 202120 Jul, Evening shiftMathematicsMediumIntegral Calculus369× since 2002

If the real part of the complex number

{(1 - \cos \theta + 2i\sin \theta )^{ - 1}}

{1 \over 5}

for

\theta \in (0,\pi )

, then the value of the integral

\int_0^\theta {\sin x} dx

is equal to:

JEE Main 2021 · 20 Jul, Evening shift · Q3408

JEE Main 202120 Jul, Evening shiftMathematicsMediumIntegral Calculus369× since 2002

If the real part of the complex number

{(1 - \cos \theta + 2i\sin \theta )^{ - 1}}

{1 \over 5}

for

\theta \in (0,\pi )

, then the value of the integral

\int_0^\theta {\sin x} dx

is equal to: