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

The integral from 1 to 2 of (x^2+x^4)/(x^2) is 10/3

Popular >

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

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

\frac{10}{3}

Decimal

3.33333 \dots

Solution steps

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

Expand

\frac{x ^{2} + x ^{4}}{x ^{2}} : \frac{x ^{2}}{x ^{2}} + \frac{x ^{4}}{x ^{2}}

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

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

\int_{1}^{2} \frac{x ^{4}}{x ^{2}} d x = \frac{7}{3}

= 1 + \frac{7}{3}

Simplify

1 + \frac{7}{3} : \frac{10}{3}

= \frac{10}{3}

\int_{0}^{45} 300 - 6 t d t

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

\int_{- 4}^{5} 1

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

\int_{0}^{\frac{π}{2}} 243 sin (θ) d θ

What is the integral from 1 to 2 of (x^2+x^4)/(x^2) ?
The integral from 1 to 2 of (x^2+x^4)/(x^2) is 10/3