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

The integral from 0 to pi/2 of 2sin(x)cos(x) is 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/2 of 2sin(x)cos(x)

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

1

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

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

= 2 \cdot \int_{0}^{1} u d u

Apply the Power Rule

: [\frac{u ^{2}}{2}]_{0}^{1}

= 2 [\frac{u ^{2}}{2}]_{0}^{1}

Compute the boundaries:

\frac{1}{2}

= 2 \cdot \frac{1}{2}

Simplify

= 1

\int_{x^{2}}^{x^{4}} u d u

\int_{1}^{4} (x^{2} + 2 x - 5) d x

\int_{0}^{3} - x^{2} + 2 x + 3 d x

\int_{0}^{4} (\frac{1}{9}) d x

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

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