ФЫ В А ПРО ВА ПРО Л ДЗАПРОЛДЖЫВАПРЯЧСМИТНЧСМИТЬБАСМИТЬБЮ ЯЧСмиDON'T USE AI | DON'T USE AI [DON'T USE AI | DON'T USE AI | DON'T USE AISOLVE STEP BY STEP IN DIGITALSolve by the method of integrals with sines andcosines:f3e3x sin²(e3x) dxFORMATУКЕНГШУИЦУКЕНГШУКЕНГШЩЗКЕНГШ щ.УКЕНГШУЙЦУКЕНГШУКЕНГШЩЗКЕНГШЩ:IBA ПPO» B ФЫ В А П Р О ВАПРОЛДЗАПРОЛДСМИТНЧСМИТЯЧСМИТНЧСМИТЬБНСМИТЕ"

Given integral is Let, Then, [ since, ]substitute the above values in the given integration we get,…

Answered: Solve by the method of integrals with…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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ФЫ В А ПРО ВА ПРО Л ДЗАПРОЛДЖЫВАПР
ЯЧСМИТНЧСМИТЬБАСМИТЬБЮ ЯЧСми
DON'T USE AI | DON'T USE AI [DON'T USE AI | DON'T USE AI | DON'T USE AI
SOLVE STEP BY STEP IN DIGITAL
Solve by the method of integrals with sines and
cosines:
f3e3x sin²(e3x) dx
FORMAT
УКЕНГШУИЦУКЕНГШУКЕНГШЩЗКЕНГШ щ.
УКЕНГШУЙЦУКЕНГШУКЕНГШЩЗКЕНГШЩ:
IBA ПPO» B ФЫ В А П Р О ВАПРОЛДЗАПРОЛД
СМИТНЧСМИТЯЧСМИТНЧСМИТЬБНСМИТЕ
"

Expert Solution

Step 1: Define the substitution

Given integral is $integral 3 e to the power of 3 x end exponent sin squared left parenthesis e to the power of 3 x end exponent right parenthesis d x$

Let, $e to the power of 3 x end exponent equals u$

Then, $3 e to the power of 3 x end exponent d x equals d u$ [ since, $fraction numerator d over denominator d x end fraction left parenthesis e to the power of a x end exponent right parenthesis equals a e to the power of a x end exponent$ ]

substitute the above values in the given integration we get,

$integral 3 e to the power of 3 x end exponent sin squared left parenthesis e to the power of 3 x end exponent right parenthesis d x equals integral sin squared left parenthesis e to the power of 3 x end exponent right parenthesis left curly bracket 3 e to the power of 3 x end exponent d x right curly bracket$

$equals integral sin squared u space d u$