What is the integral of-sqrt(0.06(60-t)) ?

The integral of-sqrt(0.06(60-t)) is 0.16329…(60-t)^{3/2}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of-sqrt(0.06(60-t))

\int - 0.06 (60 - t) d t

0.16329 \dots (60 - t)^{\frac{3}{2}} + C

Solution steps

\int - 0.06 (60 - t) d t

Take the constant out:

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

= - \int 0.06 (60 - t) d t

Simplify

0.06 (60 - t) : 0.24494 \dots 60 - t

= - \int 0.24494 \dots 60 - t d t

Take the constant out:

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

= - 0.24494 \dots \cdot \int 60 - t d t

Apply u-substitution

= - 0.24494 \dots \cdot \int - u d u

Take the constant out:

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

= - 0.24494 \dots (- \int u d u)

Apply the Power Rule

= - 0.24494 \dots (- \frac{2}{3} u^{\frac{3}{2}})

Substitute back

u = 60 - t

= - 0.24494 \dots (- \frac{2}{3} (60 - t)^{\frac{3}{2}})

Simplify

- 0.24494 \dots (- \frac{2}{3} (60 - t)^{\frac{3}{2}}) : 0.16329 \dots (60 - t)^{\frac{3}{2}}

= 0.16329 \dots (60 - t)^{\frac{3}{2}}

Add a constant to the solution

= 0.16329 \dots (60 - t)^{\frac{3}{2}} + C

What is the integral of-sqrt(0.06(60-t)) ?
The integral of-sqrt(0.06(60-t)) is 0.16329…(60-t)^{3/2}+C