Evaluate: int_(-2)^2(ti+t^2j+t^3k)dt

bergvolk0k

bergvolk0k

Answered question

2022-10-23

Evaluate:
2 2 ( t i + t 2 j + t 3 k ) d t

Answer & Explanation

rcampas4i

rcampas4i

Beginner2022-10-24Added 22 answers

Solution:
2 2 ( t i + t 2 j + t 3 k ) d t = [ t 3 3 i + t 3 3 j t 4 4 k ] 2 2 = [ 2 3 3 i + 2 3 3 j 2 4 4 k ] [ ( 2 ) 3 3 i + ( 2 ) 3 j ( 2 ) 4 4 k 3 ] = [ 8 3 i + 8 3 j 4 k ] [ 8 3 i 8 3 j 4 k ] = 8 3 i + 8 3 j 4 k + 8 3 i + 8 3 j + 4 k = 16 3 i + 16 3 j = 16 3 ( i + j )

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