What is the integral from 0 to 4 of pi((20-5x)/4)^2 ?

The integral from 0 to 4 of pi((20-5x)/4)^2 is (100pi)/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 4 of pi((20-5x)/4)^2

\int_{0}^{4} π (\frac{20 - 5 x}{4})^{2} d x

\frac{100 π}{3}

Decimal

104.71975 \dots

Solution steps

\int_{0}^{4} π (\frac{20 - 5 x}{4})^{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}^{4} (\frac{20 - 5 x}{4})^{2} d x

Apply Integration By Parts

: [\frac{1}{16} x (20 - 5 x)^{2} - \int - \frac{5}{8} x (- 5 x + 20) d x]_{0}^{4}

= π [\frac{1}{16} x (20 - 5 x)^{2} - \int - \frac{5}{8} x (- 5 x + 20) d x]_{0}^{4}

\int - \frac{5}{8} x (- 5 x + 20) d x = - \frac{5}{8} (- \frac{5 x ^{3}}{3} + 10 x^{2})

= π [\frac{1}{16} x (20 - 5 x)^{2} - (- \frac{5}{8} (- \frac{5 x ^{3}}{3} + 10 x^{2}))]_{0}^{4}

Simplify

π [\frac{1}{16} x (20 - 5 x)^{2} - (- \frac{5}{8} (- \frac{5 x ^{3}}{3} + 10 x^{2}))]_{0}^{4} : π [\frac{1}{48} (25 x^{3} - 300 x^{2} + 1200 x)]_{0}^{4}

= π [\frac{1}{48} (25 x^{3} - 300 x^{2} + 1200 x)]_{0}^{4}

Compute the boundaries:

\frac{100}{3}

= π \frac{100}{3}

Simplify

= \frac{100 π}{3}

\int_{0}^{1} f (u) d u

\int_{1}^{6} \frac{8}{x} d x

\int_{- x}^{x} 1 + t^{2} d t

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

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

What is the integral from 0 to 4 of pi((20-5x)/4)^2 ?
The integral from 0 to 4 of pi((20-5x)/4)^2 is (100pi)/3