Given that f(1)=1.548 and f'(x)=sin(x^2), what is f(7)?

Question

This is a question on a packet for my calc ab class but I just can't get the right answer

Answer 1

By the Fundamental Theorem of Calculus,

f(b) - f(a) = ∫_{(from a to b)}f'(x)dx

 

f(7) = f(1) + f(7) - f(1)

 

      = 1.548 + ∫_{(from 1 to 7)}f'(x)dx

 

      = 1.548 + ∫_{(from 1 to 7)} sin(x²)dx

 

You can use your graphing calculator to approximate the integral above and then answer the question. Alternatively, using Wolfram Alpha, the value of the integral is approximately 0.295619.

 

So, f(7) ≈ 1.548 + 0.295619 ≈ 1.844