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

The integral from 0 to 2 of sin^2(x) is 1-1/4 sin(4)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

1 - \frac{1}{4} sin (4)

Decimal

1.18920 \dots

Solution steps

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

Rewrite using trig identities

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

Take the constant out:

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

= \frac{1}{2} \cdot \int_{0}^{2} 1 - cos (2 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

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

\int_{0}^{2} 1 d x = 2

\int_{0}^{2} cos (2 x) d x = \frac{1}{2} sin (4)

= \frac{1}{2} (2 - \frac{1}{2} sin (4))

Simplify

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

= 1 - \frac{1}{4} sin (4)

\int_{0}^{1} u d u

\int_{0}^{3} \frac{1}{1 + 1 + x} d x

\int_{- 1}^{2} (x) d x

\int_{- 4}^{4} 2 x^{3} - 2 x d x

\int_{2}^{4} x ln (x) d x

What is the integral from 0 to 2 of sin^2(x) ?
The integral from 0 to 2 of sin^2(x) is 1-1/4 sin(4)