What is the integral from 0 to θ of (2x)/(θ^2) ?

The integral from 0 to θ of (2x)/(θ^2) 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 θ of (2x)/(θ^2)

\int_{0}^{θ} \frac{2 x}{θ ^{2}} d x

1

Solution steps

\int_{0}^{θ} \frac{2 x}{θ ^{2}} d x

Take the constant out:

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

= \frac{2}{θ ^{2}} \cdot \int_{0}^{θ} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{0}^{θ}

= \frac{2}{θ ^{2}} [\frac{x ^{2}}{2}]_{0}^{θ}

Compute the boundaries:

\frac{θ ^{2}}{2}

= \frac{2}{θ ^{2}} \cdot \frac{θ ^{2}}{2}

Simplify

= 1

\int_{0}^{π} 3 sec^{2} (x) d x

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

\int_{0}^{b} e^{- x} d x

\int_{- 2}^{1} x^{2} + 2 x + 1 d x

\int_{- 1}^{2} x + 2 d x

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