What is the integral from 0 to 0.5 of sin^2(x) ?

The integral from 0 to 0.5 of sin^2(x) is 0.03963…

Popular >

integral from 0 to 0.5 of sin^2(x)

\int_{0}^{0.5} sin^{2} (x) d x

0.03963 \dots

Solution steps

\int_{0}^{0.5} sin^{2} (x) d x

Rewrite using trig identities

= \int_{0}^{0.5} \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}^{0.5} 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}^{0.5} 1 d x - \int_{0}^{0.5} cos (2 x) d x)

\int_{0}^{0.5} 1 d x = 0.5

\int_{0}^{0.5} cos (2 x) d x = \frac{1}{2} sin (1)

= \frac{1}{2} (0.5 - \frac{1}{2} sin (1))

Simplify

\frac{1}{2} (0.5 - \frac{1}{2} sin (1)) : 0.03963 \dots

= 0.03963 \dots

\int_{0}^{x} \frac{1}{( 1 - x ) ^{2.5}} d x

\int_{0}^{x} 20 (\frac{3}{2} x)^{\frac{1}{3}} d x

\int_{0}^{x} sin (x - t) t e^{t} d t

\int_{- 1}^{2} [4 x^{3} - 6 x^{2} + 1] d x

\int_{0}^{t} \frac{y}{y + 2} d y

What is the integral from 0 to 0.5 of sin^2(x) ?
The integral from 0 to 0.5 of sin^2(x) is 0.03963…