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

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

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/4 of 4sin^2(x)

\int_{0}^{\frac{π}{4}} 4 sin^{2} (x) d x

\frac{π}{2} - 1

Decimal Notation

0.57079 \dots

Solution steps

\int_{0}^{\frac{π}{4}} 4 sin^{2} (x) d x

Take the constant out:

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

= 4 \cdot \int_{0}^{\frac{π}{4}} sin^{2} (x) d x

Rewrite using trig identities

= 4 \cdot \int_{0}^{\frac{π}{4}} \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

= 4 \cdot \frac{1}{2} \cdot \int_{0}^{\frac{π}{4}} 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

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

\int_{0}^{\frac{π}{4}} 1 d x = \frac{π}{4}

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

= 4 \cdot \frac{1}{2} (\frac{π}{4} - \frac{1}{2})

Simplify

4 \cdot \frac{1}{2} (\frac{π}{4} - \frac{1}{2}) : \frac{π}{2} - 1

= \frac{π}{2} - 1

h \to 0 lim ((1 + 5 h)^{\frac{1}{h}})

\frac{d}{d x} (y^{2} - x^{2})

\int e^{5 x + e^{5 x}} d x

\frac{s}{2 s ^{2} + 4 s + 3}

\frac{d y}{d x} = \frac{x 1 - y ^{2}}{y 1 - x ^{2}}

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