integral problem

Question

assume F'(t)= sin(t)cos(t) and F(0)=5. find F(b) for b=0, 0.5, 1, 1.5, 2, 2.5, and 3. Round to three decimal places.

Hint: you are given that F(0)=5. using the fundamental theorem of calculus you can find F (0.5)

I found the antiderivative and plugged in all the b values and then added them to the previous value to satisfy the integral but I'm still getting the answers incorrect.

Answer 1

F(t) = ∫sin(t)cos(t)dt = u = sint

du = costdt

= ∫udu

= 1/2u² + C

= 1/2sin²t + C

F(0) = 1/2sin²0 + C = 5 ; C = 5

F(t) = 1/2sin²t + 5

You should now be able to plug in the requested values for b.

Answer 2

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