Question

The area of the first quadrant region bounded by the y-axis, the line y=4-x and the graph of y=x-cosx is approximately
A 4.50 units ^2
B 4.54 ...
C 4.56 ...
D 4.58...
E 5.00 ...
Answer is B please explain how to get to the answer ! This is a calculator question.

Answer 1

Can you do an integral on this calculator?

Answer 2

Yes

Answer 3

Okay, then set it up. \(\int\limits_{0}^{1.858246}(4-x)-(x-\cos(x))\;dx\)

Finding the intersection was the tricky part, but I expect your TRACE facility will do that for you, no?

Answer 4

Yes ..how did u find the 1.858..?

Answer 5

There are lots of ways. Your calculator should do it. Put both traces on the same set of coordinate axes and see where they intersect. You can then activate the little pointer and follow one of the curves around until you find it.

Answer 6

Okay! How do you specifically get 4.54 because the first time I did it I got 4.938

Answer 7

We did not read sufficiently carefully. It says FIRST QUADRANT. This gives two different integrals - one for [0,0.739] and the other for [0.739,1.855]. Give it another go.

Answer 8

So how would you input that into the calculator?

Answer 9

How did you get 4.938? Do it the same way, just in two pieces.

\(\int\limits_{0}^{0.739}(4-x)\;dx + \int\limits_{0.739}^{1.855}(4-x)-(x-\cos(x))\;dx\)

The hardest part, now, is just keeping track.

Answer 10

I got it ! Okay how did you get your points. (0, .739) and (.739, 1.855) ?

Answer 11

Same answer. There are many ways. Your calculator will do it for you. The TRACE feature will probably be sufficient. Get the little cursor on the curve and follow it around until you find the point you want. The calculator should give you the coordinates as you go.

Answer 12

Okay thank you so much for your help!