Question

Please help me with a Calc AB multiple choice. Happy holidays

Answer 1

By the fundamental theorem of calculus (FTC), we can say

`\displaystyle \int_(a)^(b)f'(t)dt = f(b) - f(a)`

`\displaystyle \int_(0)^(4)f'(t)dt = f(4) - f(0)`

This means,

`\displaystyle \int_(0)^(4)f'(t)dt = 8`

`\displaystyle f(4) - f(0) = 8`

`\displaystyle f(4) - 5 = 8`

`\displaystyle f(4) - 5+5 = 8+5`

`\displaystyle f(4) = 13`

So that's why the answer is choice E) 13