What is the integral from 0 to 2 of 2tsin(2pit) ?

The integral from 0 to 2 of 2tsin(2pit) is -2/pi

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 2 of 2tsin(2pit)

\int_{0}^{2} 2 t sin (2 π t) d t

- \frac{2}{π}

Decimal Notation

- 0.63661 \dots

Solution steps

\int_{0}^{2} 2 t sin (2 π t) d t

Take the constant out:

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

= 2 \cdot \int_{0}^{2} t sin (2 π t) d t

Apply Integration By Parts

: [- \frac{1}{2 π} t cos (2 π t) - \int - \frac{1}{2 π} cos (2 π t) d t]_{0}^{2}

= 2 [- \frac{1}{2 π} t cos (2 π t) - \int - \frac{1}{2 π} cos (2 π t) d t]_{0}^{2}

\int - \frac{1}{2 π} cos (2 π t) d t = - \frac{1}{4 π ^{2}} sin (2 π t)

= 2 [- \frac{1}{2 π} t cos (2 π t) - (- \frac{1}{4 π ^{2}} sin (2 π t))]_{0}^{2}

Simplify

= 2 [- \frac{1}{2 π} t cos (2 π t) + \frac{1}{4 π ^{2}} sin (2 π t)]_{0}^{2}

Compute the boundaries:

- \frac{1}{π}

= 2 (- \frac{1}{π})

Simplify

= - \frac{2}{π}

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

\int_{0}^{4} \frac{1}{2} x^{2} d x

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

\int_{0}^{2 - x} \frac{3}{4} x d x

\int_{0.5}^{1.5} (1 4^{2 x}) d x

What is the integral from 0 to 2 of 2tsin(2pit) ?
The integral from 0 to 2 of 2tsin(2pit) is -2/pi