What is the integral from 0 to 5 of |t^2+2t-15| ?

The integral from 0 to 5 of |t^2+2t-15| is 137/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 5 of |t^2+2t-15|

\int_{0}^{5} t^{2} + 2 t - 15 d t

\frac{137}{3}

Decimal

45.66666 \dots

Solution steps

\int_{0}^{5} t^{2} + 2 t - 15 d t

Eliminate Absolutes

= \int_{0}^{3} - t^{2} - 2 t + 15 d t + \int_{3}^{5} t^{2} + 2 t - 15 d t

\int_{0}^{3} - t^{2} - 2 t + 15 d t = 27

\int_{3}^{5} t^{2} + 2 t - 15 d t = \frac{56}{3}

= 27 + \frac{56}{3}

Simplify

27 + \frac{56}{3} : \frac{137}{3}

= \frac{137}{3}

\int_{0}^{2} \frac{1}{( 2 - x ) ^{\frac{5}{2}}} d x

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

\int_{- 2}^{1} (2 x^{3} + 4 x^{2} - x + 3) d x

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

\int_{1}^{8} \frac{1}{t} d t

What is the integral from 0 to 5 of |t^2+2t-15| ?
The integral from 0 to 5 of |t^2+2t-15| is 137/3