What is the integral of sqrt(1-(sin(x))^2) ?

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

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integral of sqrt(1-(sin(x))^2)

\int 1 - (sin (x))^{2} d x

sin (x) + C

Solution steps

\int 1 - (sin (x))^{2} d x

Rewrite using trig identities

= \int cos^{2} (x) d x

cos^{2} (x) = (cos (x)),

assuming

cos (x) \geq 0

= \int cos (x) d x

Use the common integral:

\int cos (x) d x = sin (x)

= sin (x)

Add a constant to the solution

= sin (x) + C

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