Integration

1.) Find Solution. We befuddle Set  . hence we have  which implies deviation back to the inconstant x, we get 2.) 3.)      Now recall the trig individuation,                                        4.)   5.)        6.)       7.) 7.)   8.)   9.) 10.) in this form we whoremonger do the inbuilt victimization the substitution .  Doing this gives,                                                  11.)          12.)             13.)         1. Lop turned a se sit outt-squared(x) factor and move it to the right. 2. Convert the remaining se gougets to tangents with the Pythagorean indistinguishability, 3. ferment by substitution, where u = tan(x) and 14.) Making the substitution u =  ejaculate x, du = cos xdx and using the identity , we have got        15.) Using identities  and , we can write:       depend the underlyings in the latter expression.        To find the estimable , we make the substitution u = sin 2x, du = 2cos 2xdx. Then        Hence, the sign built-in is        16.) Calculate the integral . Solution. We can write:      transubstantiate the integrand using the identities       We get        17.) Evaluate the integral . Solution.

We delectation the identity  to transform the integral. This yields        Calculate the integral . Solution. Using the identity , we have         18.) Calculate the integral . ! Solution. We use the decline formula        Hence,        The integral  is a table integral which is have-to doe with to . (It can be easily found usingthe universal trigonometric substitution .) As a result, the integral becomes        18.) Evaluate the integral . Solution. We use the reduction formula        Hence,        20. Compute . Solution.        21.) Compute . Solution. Use the identity . Then        Since  (see Example 9) and  is a table integral equal to , we begin the following complete answer:        21.)If you want to get a full essay, order it on our website: OrderEssay.net

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