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

The integral from 1 to 4 of sqrt(x)-1/(x^2) is 47/12

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 sqrt(x)-1/(x^2)

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

\frac{47}{12}

Decimal Notation

3.91666 \dots

Solution steps

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

\int_{1}^{4} x d x = \frac{14}{3}

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

= \frac{14}{3} - \frac{3}{4}

Simplify

\frac{14}{3} - \frac{3}{4} : \frac{47}{12}

= \frac{47}{12}

\int_{- 2}^{3} (4 x - 3) (x - 3) d x

\int_{- 1}^{1} (x^{5} - x^{6}) d x

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

\int_{0}^{2} - 2 x + 2 d x

\int_{0}^{1} \frac{1}{1 + 2 x} d x

What is the integral from 1 to 4 of sqrt(x)-1/(x^2) ?
The integral from 1 to 4 of sqrt(x)-1/(x^2) is 47/12