Question
How do you complete the proof for the integration of dx/sqrt(a^2 - x^2) = arcsin (x/a) + C.
a is a constant.
a is a constant.
Answers
Count Iblis
Substitute x = a sint(t) in
dx/sqrt(a^2 - x^2)
dx = a cos(t) dt
sqrt(a^2 - x^2) = a |cos(t)|
Because x is between -a and a, t can be chose to be between -pi/2 and pi/2, which means that cos(t) is postive, so we can omit the absolute value signs. This means that:
dx/sqrt(a^2 - x^2) = dt
The integral is thus t + C=
arcsin (x/a) + C
dx/sqrt(a^2 - x^2)
dx = a cos(t) dt
sqrt(a^2 - x^2) = a |cos(t)|
Because x is between -a and a, t can be chose to be between -pi/2 and pi/2, which means that cos(t) is postive, so we can omit the absolute value signs. This means that:
dx/sqrt(a^2 - x^2) = dt
The integral is thus t + C=
arcsin (x/a) + C