Evaluate the following integrals
(i) `int_(R)^(oo)(GMm)/(x^(2))dx` (ii) `int_(r_(1))^(r_(2))-k(q_(1)q_(2))/(x^(2))dx` (iii) `int_(u)^(v)Mvdv`
(iv) `int_(0)^(oo)x^(-1//2)dx` (v) `int_(0)^(pi//2)sin x dx` (vi) `int_(0)^(pi//2)cos x dx`
(vii) `int_(-pi//2)^(pi//2) cos x dx`

Explanation

Let's evaluate the integrals step by step.

### (i) Evaluate \( \int_{r}^{\infty} \frac{GMm}{x^2} \, dx \)

1. **Set up the integral**:
\[ \int_{r}^{\infty} \frac{GMm}{x^2} \, dx \]
...