Question

1. Use an appropriate extit{u}-substitution along with the rule ( int frac{du}{a^2 + u^2} = frac{1}{a} arctan{left(frac{u}{a} ight)} + C ), to evaluate the integral (a) ( int frac{dx}{16 + 4x^2} ). (b) ( int_0^1 frac{dx}{16 + 4x^2} ).

          1. Use an appropriate 	extit{u}-substitution along with the rule
( int frac{du}{a^2 + u^2} = frac{1}{a} arctan{left(frac{u}{a}
ight)} + C ),
to evaluate the integral
(a) ( int frac{dx}{16 + 4x^2} ).
(b) ( int_0^1 frac{dx}{16 + 4x^2} ).

$1. Use an appropriate extitu-substitution along with the rule ( int fracdua^2 + u^2 = frac1a arctanleft(fracua ight) + C ), to evaluate the integral (a) ( int fracdx16 + 4x^2 ). (b) ( int0^1 fracdx16 + 4x^2 ).$

Added by Raven W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Shannon K

02/22/2022

Step 1

However, the integral is not clearly defined in the question. Assuming the integral is ∫(G+11-tu)15F dt, we can choose u = G+11-tu. Then, du = -dt. We substitute these into the integral and get -∫15F du. Show more…

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