What is the integral from 1/2 to 2 of 2/x-1/2 x ?

The integral from 1/2 to 2 of 2/x-1/2 x is 4ln(2)-15/16

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integral from 1/2 to 2 of 2/x-1/2 x

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

4 ln (2) - \frac{15}{16}

Decimal

1.83508 \dots

Solution steps

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

\int_{\frac{1}{2}}^{2} \frac{2}{x} d x = 4 ln (2)

\int_{\frac{1}{2}}^{2} \frac{1}{2} x d x = \frac{15}{16}

= 4 ln (2) - \frac{15}{16}

\int \frac{4 - 32 x}{81 - 16 x ^{2}} d x

x \to 3 lim (\frac{9 + x}{3 - x})

x \to \infty lim (8 x + 5)

f (x) = - x^{2} - 3 x + 4

y^{^{'}} + x^{2} y = 1

What is the integral from 1/2 to 2 of 2/x-1/2 x ?
The integral from 1/2 to 2 of 2/x-1/2 x is 4ln(2)-15/16