What is the integral from 1 to t of 15x^{-3} ?

The integral from 1 to t of 15x^{-3} is 15(-1/(2t^2)+1/2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 1 to t of 15x^{-3}

\int_{1}^{t} 15 x^{- 3} d x

15 (- \frac{1}{2 t ^{2}} + \frac{1}{2})

Solution steps

\int_{1}^{t} 15 x^{- 3} d x

Take the constant out:

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

= 15 \cdot \int_{1}^{t} x^{- 3} d x

Apply the Power Rule

= 15 [- \frac{1}{2 x ^{2}}]_{1}^{t}

Compute the boundaries:

- \frac{1}{2 t ^{2}} + \frac{1}{2}

= 15 (- \frac{1}{2 t ^{2}} + \frac{1}{2})

What is the integral from 1 to t of 15x^{-3} ?
The integral from 1 to t of 15x^{-3} is 15(-1/(2t^2)+1/2)