What is the integral of sqrt(1-4(1/2 sin(x))^2) ?

The integral of sqrt(1-4(1/2 sin(x))^2) is sin(x)+C

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integral of sqrt(1-4(1/2 sin(x))^2)

\int 1 - 4 (\frac{1}{2} sin (x))^{2} d x

sin (x) + C

Solution steps

\int 1 - 4 (\frac{1}{2} sin (x))^{2} d x

Simplify

1 - 4 (\frac{1}{2} sin (x))^{2} : cos^{2} (x)

= \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

ln (1 - 5 x)

f (t) = e^{2 (t - 2)}

f (x) = \frac{1 + x}{( 2 x ^{2} + 1 ) ^{2}}

\frac{d}{d t} (t^{3} - 5 t^{2} + 9 t)

y = 2 x + 2, y = x^{2} - 2

What is the integral of sqrt(1-4(1/2 sin(x))^2) ?
The integral of sqrt(1-4(1/2 sin(x))^2) is sin(x)+C