Use the table of integrals at the back of the text to evaluate the integrals \int 8\sin(4t)\sin(\frac{t}{2})dt

Khaleesi Herbert 2020-12-28 Answered
Use the table of integrals at the back of the text to evaluate the integrals 8sin(4t)sin(t2)dt
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Expert Answer

yunitsiL
Answered 2020-12-29 Author has 108 answers
Step 1
Let the given integral is,
8sin(4t)sin(t2)dt
By using the formula,
sin(a)sin(b)=cos(a+b)+cos(ab)2
8(cos(4tt2)cos(4t+t2)2)dt
8(cos(7t2)cos(9t2)2)dt
Step 2
By separating the integrals,
82(cos(7t2))dt(cos(9t2))dt
Simplifying this,
8sin(4t)sin(t2)dt=4[27sin(7t2)29sin(9t2)]+C
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Jeffrey Jordon
Answered 2021-11-08 Author has 2064 answers

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