What is the integral from 1 to 4 of 3x^2-4+4/(x^2) ?

The integral from 1 to 4 of 3x^2-4+4/(x^2) is 54

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 1 to 4 of 3x^2-4+4/(x^2)

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

54

Solution steps

\int_{1}^{4} 3 x^{2} - 4 + \frac{4}{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

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

\int_{1}^{4} 3 x^{2} d x = 63

\int_{1}^{4} 4 d x = 12

\int_{1}^{4} \frac{4}{x ^{2}} d x = 3

= 63 - 12 + 3

Simplify

= 54

\int_{- 2}^{7} (- ∣ x ∣) d x

\int_{0}^{10} - 6.4 (0. 9^{x}) d x

\int_{1}^{y} \frac{2}{y ^{3}} d y

\int_{0}^{3} (6 - 2 x) d x

\int_{0}^{1} x^{\frac{1}{3}} - x^{\frac{1}{2}} d x

What is the integral from 1 to 4 of 3x^2-4+4/(x^2) ?
The integral from 1 to 4 of 3x^2-4+4/(x^2) is 54