Question

Evaluate. ſ (128 +7+-5) dt 0 24t + 7 + C O 6P + 7t2 - 5t + c O 12+ + 7t2 - 5t + C O4 + 72 - St+C

Answer 1

$4t^3+\frac{7}{2}t^2-5t+C$

Explanation

$\int (12t^2+7t-5)\text{ d t}$

Step 1

separate the terms

$\int (12t^2+7t-5)\mathrm{d}t=\int 12t^2dt+\int 7tdt-\int 5\text{ d t}$

then, solve each integer:

remeber

$\int ax^ndx=\frac{(a)}{n+1}x^{n+1}$

hence,

$\begin{gathered} \int 12t^2dt+\int 7tdt-\int 5\text{ d }t=(\frac{12}{3})t^{2+1}+\frac{7}{2}t^{1+1}-\frac{5}{1}t^{0+1} \\ \int 12t^2dt+\int 7tdt-\int 5\text{ d }=4t^3+\frac{7}{2}t^2-5t+C \end{gathered}$

I hope this helps you