Evaluate the following integrals
(i) `int_(R)^(oo)(GMm)/(x^(2))dx`
(ii) `int_(r_(1))^(r_(2)) -k(q_1q_2)/(x^(2))dx`
(iii) `int_(u)^(v) Mv dv`
(iv) `int_(0)^(oo) x^(-1//2) dx`
(v) `int_(0)^(pi//2) sinx dx `
(vi) `int_(0)^(pi//2) cosx dx`
(vii) `int_(-pi//2)^(pi//2) cos x dx`

Options

A. `(2, -2)`
B. `(2, 2)`
C. `(-2, 2)`
D. `(-2, -2)`

Answer

B, D

Explanation

Let catching point be `(x_(1), y_(1))` then, `y_(1)-x_(1)=0` and `x_(1)^(2)+y_(1)^(2)=8`
Therefore, `2x_(1)^(2)=8 rArr x_(1)^(2)=4 rArr x_(1)=+-2`, So possible points are `(2, 2)` and `(-2, -2)`.