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

The integral from 1/2 to x of 2/(t^2) is 2(-1/x+2)

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integral from 1/2 to x of 2/(t^2)

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

2 (- \frac{1}{x} + 2)

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Apply the Power Rule

: [- \frac{1}{t}]_{\frac{1}{2}}^{x}

= 2 [- \frac{1}{t}]_{\frac{1}{2}}^{x}

Compute the boundaries:

- \frac{1}{x} + 2

= 2 (- \frac{1}{x} + 2)

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