If the real part of the complex number … is … for …, then the value of the integral … is equal to:

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Definite Integration

JEE Main 2021 · 20 Jul, Evening shift · Q3408

MathematicsMedium210×since 2002Q3408

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

MathematicsMedium210×since 2002Q3408

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: