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10. Evaluate the following integrals. (a) 36-x dx If use see use the sub so that and Va2 x2 x = a sin dxa

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10. Evaluate the following integrals. (a) 36-x dx If use see use the sub so that and Va2 x2 x = a sin dxa cose de - = a cos ax x = atan dx = a sec 0 de a + x = a sec x2 a xa sec dx = a sec tan 0 de x- a = a tan 0 Please use the trigonometric substitution rule. SECTION 7.3 Trigonometric Substitution 419 / Step 4. Convert to the original variable. Since u = x + 1 and u + 2 = x + 2x + 3, Eq. (3) becomes du = x+1 (u + 2) 3/2 -2x + 2x + 3 +C Therefore, by q. (2): dx x +1 +C (x+2x+3)/2 2x+2x+3 S 7.3 SUMMARY Trigonometric substitution: 1-sino do in integrand - Square root form substati x = a sine, x + a x - a x = a tan, x = a sec, Sind Va-x x=asin@ a x+a x=atan6 Vaza axx X 2 xa x=aseco a 4 x 0.0020 ex de x x-1 = lysed x=3 sec dx=3 secotun Odo x-9=3tan 0. Sub (stan Ose ( 0) do do + = = 9 aseco do + 10 + Scos do Sing+ C Sea = 9x+C

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