aidmoong7

2021-11-19

Evaluate the indefinite integral.
$\int {t}^{\frac{-6}{11}}dt$

Ceitheart

Step 1
It is given that, $\int {t}^{\frac{-6}{11}}dt$.
We have to evaluate the indefinite integral.
Step 2
We have, $\int {t}^{\frac{-6}{11}}dt$
Now, by applying power rule: $\int {t}^{n}dt=\frac{{t}^{n+1}}{n+1}+C$, where C is arbitrary constant
So, $\int {t}^{\frac{-6}{11}}dt=\frac{{t}^{-\frac{6}{11}+1}}{-\frac{6}{11}+1}+C$
$⇒\int {t}^{-\frac{6}{11}}dt=\frac{{t}^{\frac{5}{11}}}{\frac{5}{11}}+C$
$⇒\int {t}^{-\frac{6}{11}}dt=\frac{11}{5}{t}^{\frac{5}{11}}+C$
Hence, $\int {t}^{-\frac{6}{11}}dt=\frac{11}{5}{t}^{\frac{5}{11}}+C$

juniorekze

Step 1: Move the negative sign to the left.
$\int {t}^{-\frac{6}{11}}dt$
Step 2: Use Negative Power Rule: ${x}^{-a}=\frac{1}{{x}^{a}}$.
$\int \frac{1}{{t}^{\frac{6}{11}}}dt$
Step 3: Use Power Rule: $\int {x}^{n}dx=\frac{{x}^{n+1}}{n+1}+C$.
$\frac{11{t}^{\frac{5}{11}}}{5}$
$\frac{11{t}^{\frac{5}{11}}}{5}+C$