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+(7)/(2)t^2-5t+C`

Step-by-step 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=((a))/(n+1)x^(n+1)`

hence,

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

I hope this helps you