Key to "Evaluate the indefinite integral. ∫t−611dt"

aidmoong7

Answered question

2021-11-19

Evaluate the indefinite integral.

\int t^{\frac{- 6}{11}} d t

Ceitheart

Beginner2021-11-20Added 14 answers

Step 1
It is given that,

\int t^{\frac{- 6}{11}} d t

.
We have to evaluate the indefinite integral.
Step 2
We have,

\int t^{\frac{- 6}{11}} d t

Now, by applying power rule:

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

, where C is arbitrary constant
So,

\int t^{\frac{- 6}{11}} d t = \frac{t^{- \frac{6}{11} + 1}}{- \frac{6}{11} + 1} + C

\Rightarrow \int t^{- \frac{6}{11}} d t = \frac{t^{\frac{5}{11}}}{\frac{5}{11}} + C

\Rightarrow \int t^{- \frac{6}{11}} d t = \frac{11}{5} t^{\frac{5}{11}} + C

Hence,

\int t^{- \frac{6}{11}} d t = \frac{11}{5} t^{\frac{5}{11}} + C

juniorekze

Beginner2021-11-21Added 18 answers

Step 1: Move the negative sign to the left.

\int t^{- \frac{6}{11}} d t

Step 2: Use Negative Power Rule:

x^{- a} = \frac{1}{x^{a}}

\int \frac{1}{t^{\frac{6}{11}}} d t

Step 3: Use Power Rule:

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

\frac{11 t^{\frac{5}{11}}}{5}

Step 4: Add constant.

\frac{11 t^{\frac{5}{11}}}{5} + C

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