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Region Area Ascertainment 2 (Posted on 2024-01-27)

Determine the area of the region bound by:

* y= sin x
* y= cos x
* y= tan x
with 0<=x<=π/2

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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Solution

| Comment 2 of 6 |

https://www.desmos.com/calculator/0rjas5f9oa

Let A be the x value of the intersection of cos and tan.

(A = asin((√5-1)/2)) or A = asin(φ-1)

Let B be the x value of the intersection of cos and sin. (B = π/4)

We want

I1: integral 0 to B of cos(x) dx

subtract two areas from that:

I2: integral 0 to A of [cos(x) - tan(x)] dx and

I3: integral 0 to B of sin(x) dx

I1 = √2/2

I2 = 0.37742807622

I3 = 0.292893218813

I1 - I2 - I3 = 0.036785486153

Posted by Larry on 2024-01-27 10:27:56

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