What is the integral from 7 to 25 of x^2(x-7)/(162) ?

The integral from 7 to 25 of x^2(x-7)/(162) is 379

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 7 to 25 of x^2(x-7)/(162)

\int_{7}^{25} x^{2} \frac{x - 7}{162} d x

379

Solution steps

\int_{7}^{25} x^{2} \frac{x - 7}{162} d x

Take the constant out:

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

= \frac{1}{162} \cdot \int_{7}^{25} x^{2} (x - 7) d x

Expand

x^{2} (x - 7) : x^{3} - 7 x^{2}

= \frac{1}{162} \cdot \int_{7}^{25} x^{3} - 7 x^{2} 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

= \frac{1}{162} (\int_{7}^{25} x^{3} d x - \int_{7}^{25} 7 x^{2} d x)

\int_{7}^{25} x^{3} d x = 97056

\int_{7}^{25} 7 x^{2} d x = 35658

= \frac{1}{162} (97056 - 35658)

Simplify

\frac{1}{162} (97056 - 35658) : 379

= 379

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

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

\int_{0}^{1} 12 x e^{x} d x

\int_{0}^{\frac{π}{4}} \frac{5}{cos ( x )} d x

\int_{1}^{7} \frac{15}{x ^{2} + 5 x + 4} d x

What is the integral from 7 to 25 of x^2(x-7)/(162) ?
The integral from 7 to 25 of x^2(x-7)/(162) is 379