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

The integral from 1 to 2 of ((1+t^2)/(t^4)) is 19/24

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

\int_{1}^{2} (\frac{1 + t ^{2}}{t ^{4}}) d t

\frac{19}{24}

Decimal

0.79166 \dots

Solution steps

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

Expand

\frac{1 + t ^{2}}{t ^{4}} : \frac{1}{t ^{4}} + \frac{1}{t ^{2}}

= \int_{1}^{2} \frac{1}{t ^{4}} + \frac{1}{t ^{2}} d t

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

\int_{1}^{2} \frac{1}{t ^{4}} d t = \frac{7}{24}

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

= \frac{7}{24} + \frac{1}{2}

Simplify

\frac{7}{24} + \frac{1}{2} : \frac{19}{24}

= \frac{19}{24}

What is the integral from 1 to 2 of ((1+t^2)/(t^4)) ?
The integral from 1 to 2 of ((1+t^2)/(t^4)) is 19/24