Trig Help!! (1 Viewer)

[Lukybear]

y=2sinx x
y=2 cosx

Find the exact area bounded by the curves and the xaxis, between pi and 3pi/2.

I keep on getting 4, but according to answers, thats not rite.

 

[solomarc20]

I think your problem is that you are just integrating between pi and 3pi/2. You have failed to realise that the two graphs intersect at 5pi/4. Once the graphs intersect, then their position changes. That is. Between pi and 5pi/4, y= 2sinx is above y=2cosx, but between 5pi/4 and 3pi/2, y=2cosx is above y=2sinx. If this doesn't make sense, draw the graph.

I think the solution wants you to do two separate integrals.

Integrate 2(sinx- cosx) between pi and 5pi/4, and then integrate 2(cosx -sinx) between 5pi/4 and 3pi/2, then add these together to get the total area

 

[Lukybear]

Yea i know about the pt of intersection. And i did two seperate integrals, one for sin and one for cos. Im just wondering if the answer is wrong?

 

[Lukybear]

Theyve got 4-2sqrt2

 

[Trebla]

Read the question carefully, it says the area bounded by the curves and the x-axis. This means it is NOT an area between two curves problem. It's actually the bit between the x-axis and the separate curves.

 

[Lukybear]

O thanks very much.... Brain isnt working today.