Question

If f(3)=11,f(3)=11, f′f′ is continuous, and ∫73f′(t)dt=20,∫37f′(t)dt=20, what is the value of f(7)?

Answer 1

Since
`f'` is continuous, we have by the fundamental theorem of calculus


`\displaystyle\int_3^7f'(t)\,\mathrm dt=f(7)-f(3)=20`

We're given that
`f(3)=11`, so it follows that
`f(7)=31`.