# How do you solve these integrals? help please!

May 30, 2018

See below.

#### Explanation:

a) We can rewrite as

$f \left(x\right) = {x}^{-} 2$

$\int f \left(x\right) \mathrm{dx} = \int {x}^{-} 2 \mathrm{dx} = - {x}^{-} 1 + C$

b) This is simply ${\left[- {x}^{-} 1\right]}_{1}^{3} = - \frac{1}{3} - \left(- 1\right) = - \frac{1}{3} + 1 = \frac{2}{3}$

c) The integral can be rewritten as

${\lim}_{t \to \infty} {\int}_{1}^{t} x \left(\frac{1}{x} ^ 2\right) \mathrm{dx}$

$= {\lim}_{t \to \infty} {\int}_{1}^{t} \frac{1}{x} \mathrm{dx}$

$= {\lim}_{t \to \infty} {\left[\ln x\right]}_{1}^{t}$

$= \ln \left(\infty\right) - 0$

Since $\ln \left(\infty\right) = \infty$, this integral diverges therefore cannot be evlauated.

Hopefully this helps!