Evaluate <mrow> 2 cos &#x2061;<!-- ⁡ 2 t <mo

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affizupdaftf3opg

Answered question

2022-04-10

Evaluate 2 cos ( 2 t ) 3 ( sin ( 2 t ) 2 ) 9  d t.

Answer & Explanation

Carolyn Farmer

Carolyn Farmer

Beginner2022-04-11Added 16 answers

Since 23 is constant with respect to t, move 23 out of the integral.

23cos(2t)(sin(2t)-2)9dt

Let u2=sin(2t)-2. Then du2=2cos(2t)dt, so 12du2=cos(2t)dt. Rewrite using u2 and du2.

231u2912du2

Simplify.

2312u29du2

Since 12 is constant with respect to u2, move 12 out of the integral.

23(121u29du2)

Simplify the expression.

13u2-9du2

By the Power Rule, the integral of u2-9 with respect to u2 is -18u2-8.

13(-18u2-8+C)

Simplify.

-124u28+C

Replace all occurrences of u2 with sin(2t)-2.

-124(sin (2t)-2)8+C

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