Answer:
D) 282
Step-by-step explanation:
Step 1: Write out the integral
[tex]\int\limits^8_1 {5t^\frac{2}{3} + 6t } \, dx[/tex]
Step 2: Find the anti-derivative for each term starting with [tex]5t^\frac{2}{3}[/tex]. To do this you add one to [tex]\frac{2}{3}[/tex] and multiply 5 by the reciprocal of that number. Then you do the same to 6t. It should equal this:
[tex]\frac{3}{5} * 5t^\frac{5}{3} + \frac{1}{2} * 6t^2[/tex][tex]]_1^{8}[/tex]
Step 3: Simplify
[tex]3t^\frac{5}{3} + 3t^2[/tex][tex]]_1^{8}[/tex]
Step 4: Solve the definite integral
[tex](3(8)^\frac{5}{3} + 3(8)^2)-(3(1)^\frac{5}{3} + 3(1)^2)[/tex]
[tex](96+192)-(3+3)[/tex]
[tex](288-6)=282[/tex]
Step 5: 282 would be your answer!
