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

The integral from 1 to 2 of (2+y^2)/(y^2) is 2

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integral from 1 to 2 of (2+y^2)/(y^2)

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

2

Solution steps

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

Expand

\frac{2 + y ^{2}}{y ^{2}} : \frac{2}{y ^{2}} + 1

= \int_{1}^{2} \frac{2}{y ^{2}} + 1 d y

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{2}{y ^{2}} d y + \int_{1}^{2} 1 d y

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

\int_{1}^{2} 1 d y = 1

= 1 + 1

Simplify

= 2

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What is the integral from 1 to 2 of (2+y^2)/(y^2) ?
The integral from 1 to 2 of (2+y^2)/(y^2) is 2