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

The integral from 1 to 2 of x^2-1/(4x^2) is 53/24

Popular >

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

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

\frac{53}{24}

Solution steps

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

\int_{1}^{2} x^{2} d x = \frac{7}{3}

\int_{1}^{2} \frac{1}{4 x ^{2}} d x = \frac{1}{8}

= \frac{7}{3} - \frac{1}{8}

Simplify

\frac{7}{3} - \frac{1}{8} : \frac{53}{24}

= \frac{53}{24}

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

\int_{0}^{7 π} 5 + sin (x) d x

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

\int_{0}^{x} sin (\frac{x}{y}) d x

\int_{- 3}^{- 1} - 6 x^{2} + 3 x + 7 d x

What is the integral from 1 to 2 of x^2-1/(4x^2) ?
The integral from 1 to 2 of x^2-1/(4x^2) is 53/24