Find the area of the following region y=sin x and y=sin 2x from x=0 x=pi/2
- print Print
- list Cite
Expert Answers
calendarEducator since 2012
write1,308 answers
starTop subjects are Math and Science
The formula for area between two curves is:
`A = int_a^b (y_U - y_L) dx`
The integral limits a and b are the intersection points of the two equation. To determine, use elimination method of system of equations.
Subtract the two equations to eliminate y variable.
`y = sin x`
`(-) ` `y = sin 2x`
-----------------------------
`0 = sin x - sin 2x`
To simplify, replace sin 2x with 2sinx cos x. Note that from double angle identity sin 2x = 2sin x cos x .
` 0 = sinx - 2sinx cosx`
`0 = sin x (1-2cos x)`
Then, set each...
(The entire section contains 266 words.)
Unlock This Answer Now
Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.
Related Questions
- `y = cos(x), y = sin(2x), x = 0, x = pi/2` Sketch the region enclosed by the given curves...
- 1 Educator Answer
- Sketch the region enclosed by the given curves. y = 4 cos 2x, y = 4 − 4 cos 2x, 0 ≤ x ≤ π/2...
- 1 Educator Answer
- Sketch the region bounded by the curves y=sec^2x and y=4 on the interval [-pi/2, pi/2]. Find...
- 1 Educator Answer
- Calculate (sin x)^2 + sin (2x)=0?
- 1 Educator Answer
- `y = cos(x), y = 1 - cos(x), 0<=x<=pi` Sketch the region enclosed by the given curves...
- 1 Educator Answer