A student performed a trigonometric substitution using x = 9tan(theta) . After t

Question

A student performed a trigonometric substitution using x = 9tan(theta) . After they computed the antiderivative in terms of theta, they forgot to do the last step of writing their answer in terms of x. You will show the results of the last missing step (a) Using their substitution, find the expressions for each side of the right triangle illustration. (b) If their antiderivative in terms of theta was 729sec(theta) + theta+ C , use the triangle above to express the antiderivative in terms of x. Your answer must be simplified.

Explanation / Answer

a)A=9

B=X

C=sqrt(81+x^2)

b)729sec theta +c

=729*hypotenuse/adjacent side +c

=729*(sqrt(81+x^2))/9 +c

=81sqrt(81+x^2) +c

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