rock.freak667 said:
vande060 said:
… learn all your trigonometric identities …
tiny-tim said:hi vande060!
sec2 = tan2 + 1, not t'other way round
Trig substitution is a technique used in calculus to simplify integrals involving expressions with trigonometric functions. It involves replacing trigonometric expressions with simpler expressions involving only a single variable.
Trig substitution is typically used when dealing with integrals that involve the square root of a quadratic expression or when working with integrals that contain expressions of the form (a^2 - x^2)^(1/2).
To use trig substitution, we first identify the form of the integral and then select an appropriate trigonometric substitution to replace the variable. We then use trigonometric identities to simplify the integral and solve for the original variable.
The most commonly used trig substitutions are:
1) x = a sinθ
2) x = a tanθ
3) x = a secθ
4) x = a cosθ
Where a is a constant and θ is a new variable.
Yes, there are a few rules to follow when using trig substitution:
1) Always make sure to substitute the variable back in at the end
2) Be careful with the signs of the trig functions
3) Use trig identities to simplify the integral
4) Watch out for the limits of integration and make appropriate changes
5) Check your final answer for correctness.