What is the integral of sqrt(1-sin(θ)) ?

The integral of sqrt(1-sin(θ)) is 2sqrt(sin(θ)+1)+C

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integral of sqrt(1-sin(θ))

\int 1 - sin (θ) d θ

2 sin (θ) + 1 + C

Solution steps

\int 1 - sin (θ) d θ

Apply u-substitution

: \int \frac{1}{u + 1} d u

= \int \frac{1}{u + 1} d u

Apply u-substitution

: \int \frac{1}{v} d v

= \int \frac{1}{v} d v

Simplify

\frac{1}{v} : \frac{1}{v}

= \int \frac{1}{v} d v

Simplify

= \int \frac{1}{v} d v

Apply the Power Rule

: 2 v^{\frac{1}{2}}

= 2 v^{\frac{1}{2}}

Substitute back

= 2 (sin (θ) + 1)^{\frac{1}{2}}

Apply radical rule:

= 2 sin (θ) + 1

Add a constant to the solution

= 2 sin (θ) + 1 + C

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What is the integral of sqrt(1-sin(θ)) ?
The integral of sqrt(1-sin(θ)) is 2sqrt(sin(θ)+1)+C