Find the average value of f(x) = sin(x) over the interval [0, pi]

[Frenchi33]

(a) Find the average value of the function over the given interval. (Round your answer to three decimal places.)

f(x) = sin(x), [0, pi]

I found the answer for (a) which is "0.637 (rounded to 3 decimal places)" by dividing the area "2" by the difference of the interval (pi - 0) which is "pi".

(b) Find all values of x in the interval for which the function equals its average value. (Enter your answers as a comma-separated list. Round your answers to three decimal places.)

x = ?

For part (b), I know I need to set "sin(x)" equal to ".637" or "2/pi", but I'm not getting the right decimal values when I solve for x.

Can someone tell me what it's supposed to be?

 

[ksdhart2]

I agree with your answer to part (a). Then for part (b) your set-up is good. If you graph the function y = sin(x) over the interval [0, pi] and the line y = 2/pi on the same interval, you'll see they intersect twice. So you know you'll have two solutions. Based on your post, I believe your work is as follows:

sin(x) = 2/pi
sin^-1(sin(x)) = sin^-1(2/pi)
x = sin^-1(2/pi)

That's a fairly straightforward plug-n-chug with your calculator, so I'm not sure why you're getting the wrong answers. My best guess would be that you're using the rounded value of 0.637. Try using the exact value of 2/pi and see if that gets you the right answers. Other than that, we can't really troubleshoot work we can't see. Please share with us all of your steps and all your thought processes on this problem, even the parts you know for sure are wrong. Thank you.

 

[Frenchi33]

I agree with your answer to part (a). Then for part (b) your set-up is good. If you graph the function y = sin(x) over the interval [0, pi] and the line y = 2/pi on the same interval, you'll see they intersect twice. So you know you'll have two solutions. Based on your post, I believe your work is as follows:

sin(x) = 2/pi
sin^-1(sin(x)) = sin^-1(2/pi)
x = sin^-1(2/pi)

That's a fairly straightforward plug-n-chug with your calculator, so I'm not sure why you're getting the wrong answers. My best guess would be that you're using the rounded value of 0.637. Try using the exact value of 2/pi and see if that gets you the right answers. Other than that, we can't really troubleshoot work we can't see. Please share with us all of your steps and all your thought processes on this problem, even the parts you know for sure are wrong. Thank you.

Oh, I just realized someone messed with my calculator and changed it to degree mode without my knowledge. Thanks for your time.

 

[HallsofIvy]

It is perhaps more likely that your calculator reverts to degree mode every time you turn it off and then back on again.

 

[stdnt]

I agree with your answer to part (a). Then for part (b) your set-up is good. If you graph the function y = sin(x) over the interval [0, pi] and the line y = 2/pi on the same interval, you'll see they intersect twice. So you know you'll have two solutions. Based on your post, I believe your work is as follows:

sin(x) = 2/pi
sin^-1(sin(x)) = sin^-1(2/pi)
x = sin^-1(2/pi)

That's a fairly straightforward plug-n-chug with your calculator, so I'm not sure why you're getting the wrong answers. My best guess would be that you're using the rounded value of 0.637. Try using the exact value of 2/pi and see if that gets you the right answers. Other than that, we can't really troubleshoot work we can't see. Please share with us all of your steps and all your thought processes on this problem, even the parts you know for sure are wrong. Thank you.

i am having the same exact problem, how would i get the second x value on the calculator?
i only got the 0.690

 

[HallsofIvy]

0.690 is the correct answer!

 

[Deleted member 4993]

i am having the same exact problem, how would i get the second x value on the calculator?
i only got the 0.690

Hint:

sin(Θ) = sin(π - Θ)