What is the integral from 0 to 5 of pi(-3/5 x+3)^2 ?

The integral from 0 to 5 of pi(-3/5 x+3)^2 is 15pi

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 pi(-3/5 x+3)^2

\int_{0}^{5} π (- \frac{3}{5} x + 3)^{2} d x

15 π

Decimal

47.12388 \dots

Solution steps

\int_{0}^{5} π (- \frac{3}{5} x + 3)^{2} d x

Take the constant out:

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

= π \cdot \int_{0}^{5} (- \frac{3}{5} x + 3)^{2} d x

Expand

(- \frac{3}{5} x + 3)^{2} : \frac{9 x ^{2}}{25} - \frac{18 x}{5} + 9

= π \cdot \int_{0}^{5} \frac{9 x ^{2}}{25} - \frac{18 x}{5} + 9 d x

Apply the Sum Rule:

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

= π (\int_{0}^{5} \frac{9 x ^{2}}{25} d x - \int_{0}^{5} \frac{18 x}{5} d x + \int_{0}^{5} 9 d x)

\int_{0}^{5} \frac{9 x ^{2}}{25} d x = 15

\int_{0}^{5} \frac{18 x}{5} d x = 45

\int_{0}^{5} 9 d x = 45

= π (15 - 45 + 45)

Simplify

= 15 π

\frac{t ^{3} + 3 t}{t ^{2} - 4 t + 3}

\int \frac{7}{x ( x - 7 ) ^{2}} d x

\frac{d}{d x} ((x - 100)^{3} + (x - 100)^{2} + 500)

\int 1 - y^{2} d y

\frac{d}{d x} ((x^{3} + 7)^{\frac{2}{3}})

What is the integral from 0 to 5 of pi(-3/5 x+3)^2 ?
The integral from 0 to 5 of pi(-3/5 x+3)^2 is 15pi