What is the integral from 0 to pi/2 of cos^2(t) ?

The integral from 0 to pi/2 of cos^2(t) is pi/4

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integral from 0 to pi/2 of cos^2(t)

\int_{0}^{\frac{π}{2}} cos^{2} (t) d t

\frac{π}{4}

Decimal

0.78539 \dots

Solution steps

\int_{0}^{\frac{π}{2}} cos^{2} (t) d t

Rewrite using trig identities

= \int_{0}^{\frac{π}{2}} \frac{1 + cos ( 2 t )}{2} d t

Take the constant out:

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

= \frac{1}{2} \cdot \int_{0}^{\frac{π}{2}} 1 + cos (2 t) d t

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}^{\frac{π}{2}} 1 d t + \int_{0}^{\frac{π}{2}} cos (2 t) d t)

\int_{0}^{\frac{π}{2}} 1 d t = \frac{π}{2}

\int_{0}^{\frac{π}{2}} cos (2 t) d t = 0

= \frac{1}{2} (\frac{π}{2} + 0)

Simplify

\frac{1}{2} (\frac{π}{2} + 0) : \frac{π}{4}

= \frac{π}{4}

x \to 0 + lim (x^{2} + 4)

\int x e^{e} d x

\int_{5}^{5} 10 x^{4} d x

\frac{d ^{2}}{d x ^{2}} (\frac{( x - 4 ) ( x ^{2} + 4 x + 16 )}{x ^{3}})

\frac{d y}{d x} = 10 x y

What is the integral from 0 to pi/2 of cos^2(t) ?
The integral from 0 to pi/2 of cos^2(t) is pi/4