What is the integral from 0 to 1 of cos^2(x) ?

The integral from 0 to 1 of cos^2(x) is 1/2 (1+1/2 sin(2))

integral from 0 to 1 of cos^2(x)

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

\frac{1}{2} (1 + \frac{1}{2} sin (2))

Decimal

0.72732 \dots

Solution steps

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

Rewrite using trig identities

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

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

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

= \frac{1}{2} (1 + \frac{1}{2} sin (2))

\frac{d}{d x} (ln (6 x + 1))

f (x) = x^{2} 2 x + 4

\int 3 tan (2 x) sec^{2} (2 x) d x

x^{2} \frac{d y}{d x} + x y = 3

\frac{d}{d x} (\frac{1}{( 3 + x ) ^{2}})

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