What is the integral from 0 to pi of 11sin^2(2x) ?

The integral from 0 to pi of 11sin^2(2x) is (11pi)/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to pi of 11sin^2(2x)

\int_{0}^{π} 11 sin^{2} (2 x) d x

\frac{11 π}{2}

Decimal Notation

17.27875 \dots

Solution steps

\int_{0}^{π} 11 sin^{2} (2 x) d x

Take the constant out:

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

= 11 \cdot \int_{0}^{π} sin^{2} (2 x) d x

Rewrite using trig identities

= 11 \cdot \int_{0}^{π} \frac{1}{2} (1 - cos (4 x)) d x

Take the constant out:

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

= 11 \cdot \frac{1}{2} \cdot \int_{0}^{π} 1 - cos (4 x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 11 \cdot \frac{1}{2} (\int_{0}^{π} 1 d x - \int_{0}^{π} cos (4 x) d x)

\int_{0}^{π} 1 d x = π

\int_{0}^{π} cos (4 x) d x = 0

= 11 \cdot \frac{1}{2} (π - 0)

Simplify

11 \cdot \frac{1}{2} (π - 0) : \frac{11 π}{2}

= \frac{11 π}{2}

\int (3 x - 4) d x

x^{4} - 13 x^{2} + 36

y = ln (8 x^{2} - 7 x + 9)

f (t) = e^{9 t s i n (2 t)}

y^{^{''}} + 49 y = sec^{2} (7 x)

What is the integral from 0 to pi of 11sin^2(2x) ?
The integral from 0 to pi of 11sin^2(2x) is (11pi)/2