What is the integral from 0 to pi of sqrt(1-cos(2x)) ?

The integral from 0 to pi of sqrt(1-cos(2x)) is sqrt(2)*2

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integral from 0 to pi of sqrt(1-cos(2x))

\int_{0}^{π} 1 - cos (2 x) d x

2 \cdot 2

Decimal

2.82842 \dots

Solution steps

\int_{0}^{π} 1 - cos (2 x) d x

Rewrite using trig identities

= \int_{0}^{π} 2 sin^{2} (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int_{0}^{π} sin^{2} (x) d x

Apply exponent rule:

a^{2} = ∣ a ∣

= 2 \cdot \int_{0}^{π} ∣ sin (x) ∣ d x

Eliminate Absolutes

= 2 \cdot \int_{0}^{π} sin (x) d x

Use the common integral:

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

= 2 [- cos (x)]_{0}^{π}

Compute the boundaries:

2

= 2 \cdot 2

\int 2 x + 3 d x

\frac{d}{d x} (e^{s i n (x)} cos (sin (x)))

\frac{d}{d x} (e^{0.1 x})

\frac{d}{d x} (e^{x} (2 x + 1))

\frac{d y}{d x} = 9 + 3 x

What is the integral from 0 to pi of sqrt(1-cos(2x)) ?
The integral from 0 to pi of sqrt(1-cos(2x)) is sqrt(2)*2