NDA2025MathematicsIndefinite IntegrationActual
Consider the following for the two (02) items that follow: Let the function y = (1 - x)⁻¹ , where x 2n and n is an integer. What is y , dx equal to?
Options
- A- (x/2) + c
- B- (x/2) + c
- C(x/2) + c
- D(x/2) + c
Correct answer
B. - (x/2) + c
Step-by-step solution
Given y = (1 - x)⁻¹ y = 1 1 - x Using the half-angle formula 1 - x = 2 ^2(x/2) y = 1 2 ^2(x/2) = 1 2 ^2(x/2) Integrating with respect to x : y , dx = 1 2 ^2(x/2) , dx y , dx = 1 2 ( - (x/2) 1/2 ) + c y , dx = - (x/2) + c Answer: - (x/2) + c