If f'(x)=sin[(pi*e^x)/2] abd f(0)=1, then f(2)=??
How do you do this when you can't take the integral of f'(x)

Question

amistre64 · Answer

why cant you take the integral?

anonymous · Answer

what level of precision is expected in the answer? because this could be approximated with a directional field.

amistre64 · Answer

vector fields eh..... ive seen them but havent played in them yet :)

anonymous · Answer

its a practice problem on the calculus ab course description

amistre64 · Answer

it says not to inegrate?

anonymous · Answer

Sorry, I meant slope field, is it multiple choice or open response?

amistre64 · Answer

slopes was my thought to; the slopes indicate the curve..... even outline it

anonymous · Answer

it is multiple choice..

anonymous · Answer

the choices are 
-1.819
-0.843
-0.819
0.157
1.157

anonymous · Answer

well it doesn't say don't integrate... i just don't know how to integrate it

anonymous · Answer

Then you should be able to construct f based on the slope f' at each x, and knowing that f(0) = 1, see how that process eliminates possibilities and gets you closer to selecting an answer.

anonymous · Answer

oh....that makes sense...but u don't know any other values

anonymous · Answer

That's okay, just start at f(0) = 1 and find f'(0) to know where the point next to x=0 would be and draw it on a graph.  Continue this process until you see that some values are more likely than others. Maybe this process will be enough to get down to only one choice.

amistre64 · Answer

f'(x)=sin[(pi/2)*(e^x)]  this is quite the same as sin(2*5^x)

anonymous · Answer

hi amistre....are u a teacher or a student?lol

amistre64 · Answer

both :)

anonymous · Answer

i thinks i got it...thanks

anonymous · Answer

with the slopes?

amistre64 · Answer

slopes seem easier than the integral lol

anonymous · Answer

i used a graphing calculator and graphed it from -1 to 4 to see the change in slope negative and positive to see if f(x) increases or decreases

anonymous · Answer

amistre64, please show me how to integrate sin(2*5^x)

amistre64 · Answer

lol..been working on it :)  seems a nightmare

amistre64 · Answer

integration is more of an art than a science ;)

anonymous · Answer

never mind it didn't work...the first derivative doesn't help

amistre64 · Answer

there aint no sin(ab) identities are there...