Find the integral of 4 9 </mfrac> <mrow class="MJX-TeXAtom-ORD"> &#xFEFF; </mr

Dereon Guzman

Dereon Guzman

Answered question

2022-05-02

Find the integral of 4 9  ( 2 t + 6 ) 10 with respect to t.

Answer & Explanation

mandamosppy

mandamosppy

Beginner2022-05-03Added 21 answers

Since 4 9 is constant with respect to t, move 4 9 out of the integral.
4 9 ( 2 t + 6 ) 10 d t
Let u=2t+6. Then du=2dt, so 1 2 d u = d t. Rewrite using u and du.
4 9 u 10 1 2 d u
Combine u 10 and 1 2
4 9 u 10 2 d u
Since 1 2 is constant with respect to u, move 1 2 out of the integral.
4 9 ( 1 2 u 10 d u )
Simplify.
2 9 u 10 d u
By the Power Rule, the integral of u 10 with respect to u is 1 11 u 11
2 9 ( 1 11 u 11 + C )
Simplify.
2 99 u 11 + C
Replace all occurrences of u with 2t+6
2 99 ( 2 t + 6 ) 11 + C

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