Project Overview Integrands containing the forms: √√a²-x²,√√x²-a², and √x² + a² are commonly solved using a trigonometri

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Project Overview Integrands Containing The Forms A X X A And X A Are Commonly Solved Using A Trigonometri 1 (68.66 KiB) Viewed 69 times

Project Overview Integrands containing the forms: √√a²-x²,√√x²-a², and √x² + a² are commonly solved using a trigonometric substitution. This transforms the integrand into a trigonometric integral which may be easier to evaluate. Project Requirements Identify each of the following integrals as one of the types listed above dx S. √√x²-7 dx x²√4-x² 1 S (4x²+9) ¹/² -dx For each type of integrand integral listed above, • State the trigonometric substitution to be used and the corresponding differential. • State the restrictions on theta that will keep the substitution one-to-one. • Draw the associated right triangle and label each leg and hypotenuse. • State which Pythagorean Identity will be used to simplify the integrand once the substitutions are made. • Evaluate the integral and back-substitute for the original variable. Do one integral per page. Show all of your work!