AP Calc AB Sample Problem Help (Integration)

[Inspector Gadget]

This is on the sample multiple choice questions in the section in which calculators are permitted. I tried it on my TI-89, and it didn't give an answer...just returned what was input with the integral sign and such...

Given that...

f'(x) = sin(\frac{\pi \times e^x}{2})

... and f(0) = 1, find f(2).

Can someone help?

 

[Inspector Gadget]

Forgot...

A.) -1.819
B.) -0.843
C.) -0.819
D.) 0.157
E.) 1.157

Answer: E

 

[Ebolamonk3y]

Try Numerical Integration... Nint feature that is on the TI 89...

Press f3, alpha, b, OR scroll up until you hit the bottom on the list and find Nint.

Should look like...

Nint((sin(pi*e^x/2),x,0,2) then add f(0) to get f(2)... 1.157

 

[billk]

You could also try local linear approximation:

f(x)\sim f(a)+f^\prime (x)\cdot (x-a)

which in this case would boil down to computing

1+2\sin ({{e^2 \pi}\over {2}} )

since your possible answers are all fairly different (hindsight: the correct answer is very different from the others), this estimation should give you a good enough idea to answer the question.