MATH 0240 Midterm: MATH 240 3c3-TrigonometSubstitu_Stu-23

• School: Pitt
• Department: Mathematics
• Course: MATH 0240
• Professor: All

Document Summary

In nding the area of a circle or an ellipse, an integral of the form where x xsa 2 x 2 dx. 1 sin2 cos2 sa 2 x 2 sa 2 a 2 sin2 sa 2 1 sin 2 sa 2 cos2 a cos . In general we can make a substitution of the form by using the substitution. To make our calculations simpler, we assume that has an inverse func- tion; that is, in the substitution. Rule (equation 5. 5. 4), we obtain t is one-to-one. In this case, if we replace by and by t t u x x x t t y f x dx y f t t t t dt. This kind of substitution is called inverse substitution. This can be accomplished by restricting x a sin provided that it de nes a one-to-one to lie in the interval.