How Much Work is Required to Stretch a Spring 3 Meters from Equilibrium?

[ineedhelpnow]

my final is tomorrow and my instructor gave a list of questions that will be similar to the ones on the final exam and i want to see how they should be done properly. I've been working on other problems but i can't get past these ones. thanks
a spring on a horizontal surface can be stretched 5m from equilibrium position with force 50 N. how much work is done stretching the spring 3m from the equilibrium position?evaluate the integral
$\int_{0}^{\infty} \ \frac{dx}{x^2-16}$

 

[topsquark]

a spring on a horizontal surface can be stretched 5m from equilibrium position with force 50 N. how much work is done stretching the spring 3m from the equilibrium position?

Hooke's Law says F = kx (using magnitudes). So you can use the initial information to find k. Then W = (1/2)kx^2.

evaluate the integral
$\int_{0}^{\infty} \ \frac{dx}{x^2-16}$

Hint: Use a partial fraction decomposition:
$$\frac{1}{x^2 - 16} = \frac{A}{x + 4} + \frac{B}{x - 4}$$.

-Dan

 

[Dethrone]

For the improper integral, you can also factor -1 out of the denominator which will turn it into a very familiar antiderivative :)

EDIT: It's only familiar if you know the derivatives of inverse hyperbolic functions.