Answered: "Find the indefinite integral ∫(2ti+j+9k)dt."

Yolanda Jorge

Answered question

2021-11-20

Find the indefinite integral

\int (2 t i + j + 9 k) d t

oces3y

Beginner2021-11-21Added 21 answers

Step 1
we have to find the value of the given indefinite integral

\int (2 t i + j + 9 k) d t

.
let the given integral be I.
therefore,

I = \int (2 t i + j + 9 k) d t

Step 2

I = \int (2 t i + j + 9 k) d t

= (\int 2 t d t) i + (\int d t) j + (\int 9 d t) k

= t^{2} i + t j + 9 t k + C

where C is constant of integration.
therefore the value of the given indefinite integral

\int (2 t i + j + 9 k) d t i s t^{2} i + t j + 9 t k + C

Xyle1991

Beginner2021-11-22Added 15 answers

Step 1
Regroup terms.

\int 2 i t + j + 9 k d t

Step 2
Use Sum Rule:

\int f (x) + g (x) d x = \int f (x) d x + \int g (x) d x

\int i + 9 k d t + \int 2 i t d t

Step 3
Use Power Rule:

\int x^{n} d x = \frac{x^{n + 1}}{n + 1} + C

j t + 9 k t + \int 2 i t d t

Step 4
Use Power Rule:

\int x^{n} d x = \frac{x^{n + 1}}{n + 1} + C

j t + 9 k t + i t^{2}

Step 5
Add constant.

j t + 9 k t + i t^{2} + C

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