What is the integral from 1 to 6 of t^2-4t-12 ?

The integral from 1 to 6 of t^2-4t-12 is -175/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 1 to 6 of t^2-4t-12

\int_{1}^{6} t^{2} - 4 t - 12 d t

- \frac{175}{3}

Decimal

- 58.33333 \dots

Solution steps

\int_{1}^{6} t^{2} - 4 t - 12 d t

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{1}^{6} t^{2} d t - \int_{1}^{6} 4 t d t - \int_{1}^{6} 12 d t

\int_{1}^{6} t^{2} d t = \frac{215}{3}

\int_{1}^{6} 4 t d t = 70

\int_{1}^{6} 12 d t = 60

= \frac{215}{3} - 70 - 60

Simplify

\frac{215}{3} - 70 - 60 : - \frac{175}{3}

= - \frac{175}{3}

\int_{- 7}^{8} \frac{1}{2} x d x

\int_{0}^{6} - \frac{5}{12} x^{2} - 5 x d x

\int_{- 2}^{- 1} x^{3} d x

\int_{0}^{1} (x - 1) e^{- x} d x

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

What is the integral from 1 to 6 of t^2-4t-12 ?
The integral from 1 to 6 of t^2-4t-12 is -175/3