Area Bounded By Curves y = sin(x), y = cscx^2 on pi/3 to pi/

[Shutterbug424]

I need to find the area bounded by the curves

y= sinx
y= cscx^2

pi/3 < x < pi/2

I found the region to be bound on the left by pi/3. The graph of sin x starts at (pi/3, sqrt(3/2)) and ends at 1. cscx^2 starts at (pi/3, 4/3) and also ends at 1.

Is there a formula or specific integral I should be using?

 

[mmm4444bot]

Re: Area Bounded By Curves

... cscx^2 ... What is this supposed to mean?

Please use grouping symbols to distinguish between the following.

csc(x^2)

[csc(x)]^2

-

sin x starts at (pi/3, sqrt(3/2)) Whoops -- the coordinates of this point are (?/3, sqrt(3)/2)

and ends at 1. And the coordinates of this ending point are (?/2, 1)

cscx^2 starts at (pi/3, 4/3) Okay -- I see now that "cscx^2" is supposed to mean the square of csc(x).

and also ends at 1. (?/2, 1)

Is there a formula ... [that] I should be using? Yes.

The formula is: Bounded Area = Larger Area - Smaller Area.

Do you know how to find the area underneath the curve of sin(x) from x = ?/3 to x = ?/2?

Do you know how to find the area underneath the curve of [csc(x)]^2 from x = ?/3 to x = ?/2?

Compare these two areas.

If you subtract the smaller one from the larger one, then the difference equals the area bounded between the two graphs.

If you need more help with this exercise, please show your work and try to say something about why you're stuck.

Cheers,

~ Mark

 

[Shutterbug424]

Re: Area Bounded By Curves

Thank you.

I ended up taking the integral from pi/3 to pi/2 of (cosx)^2 -sinx

The final answer I arrived at was 2- sqrt(3)/2sqrt(3)
...or approximately .07735

If you care to check it, that would be great!

 

[mmm4444bot]

Re: Area Bounded By Curves

I ended up taking the integral from pi/3 to pi/2 of (cosx)^2 - sinx This looks like more sloppy typing, to me. I'll guess that you mean (cscx)^2 - sinx.

The final answer I arrived at was [2 - sqrt(3)]/[2 sqrt(3)] ? Please use grouping symbols. (Your work is not clear, in this thread.)

... or approximately 0.07735 ? This is correct.

 

[Shutterbug424]

Re: Area Bounded By Curves

Thanks