Solving Calculus and Equation Problems

[pyromancer]

Homework Statement

Question 1 :Find the value of $$\int^{\infty}_{0}$$$$\stackrel{dx}{a^{2} + x^{2}}$$

Question 2 : Find the number of positive integral solutions of the equation :

$$x_{1}$$$$x_{2}$$$$x_{3}$$$$x_{4}$$$$x_{5}$$ = 1050

Homework Equations

Well I do not know any relevant equations.

The Attempt at a Solution

Well I tried the first question by substituting x with a(tan(y)) then I got sec$$^{12}$$ but then I don't know what to do. The second question has me stumped totally. I tried finding the factors of 1050 and then finding the permutations of the factors to get the answer but did not get it .

 

[Kurret]

Q1: hint: factor out $$\frac{1}{a^2}$$
Q2: Try again with the same method, i think it should work, it just takes time.

 

[tiny-tim]

Well I tried the first question by substituting x with a(tan(y)) then I got sec$$^{12}$$

No … did you mean sec$$^{2}$$ or sec$$^{-2}$$? … anyway, either is wrong … do it again … you must substitute for dx also.

dx = … ?

Question 2 : Find the number of positive integral solutions of the equation :

$$x_{1}$$$$x_{2}$$$$x_{3}$$$$x_{4}$$$$x_{5}$$ = 1050

This isn't calculus, is it?

What did you get as the prime factors of 1050?

Show us where you went from there …

 

[Gib Z]

Q1) You don't really even need to find the anti-derivative here. Look at your bounds of integration, how does your integrand behave...?

Q2) Just do what everyone else said. Perhaps the trouble with the calculation of the permutations comes from the repeated factor? Make sure you take that into account.