Posted by Anonymous on Friday, January 25, 2013 at 2:41am.
1. Find the area of the region between the curves y=sin(x pi/2) and y=x.
2. Find the area of the region between the curves y=sin(x), y=sin(2x), x=0, and x=pi/2.

Calculus  Reiny, Friday, January 25, 2013 at 11:42am
I will do the harder of the two
2.
If you make a sketch you will see that the curves intersect in your domain 0 ≤ x ≤ π/2
sin2x = sinx
2sinxcosx  sinx = 0
sinx(2cosx  1) = 0
sinx = 0 or cosx = 1/2
x = 0 , your left domain, or
x = π/3
so we have to do this in two parts
area = ∫(sin2x  sinx) dx from 0 to π/3 + ∫(sinx  sin2x) dx from π/3 to π/2
= [(1/2)cos2x + cosx] form 0 to π/3 + [cosx + 1/2)cos2x ] from π/3 to π/2
= (1/4 + 1/2  (1/2) + 1)) + (0 + 0 (1/2 +(1/2)(1/2))
= .... you do the arithmetic
and please check my arithmetic above, should have written it out on paper first.
Answer This Question
Related Questions
 Calculus  1. Find the area of the region between the curves y=sin(x pi/2) and y...
 Calculus  1. Find the area of the region between the curves y=sin(x pi/2) and y...
 Calculus (Area Between Curves)  Find the area of the region IN THE FIRST ...
 CalculusArea between curves  Sketch the region enclosed by the given curves. ...
 math  Roughly sketch the region enclosed by the curves y = sin x, y = cos x and...
 Calculus (Area Between Curves)  Find the area of the region IN THE FIRST ...
 Calculus Area between curves  Sketch the region enclosed by the given curves. ...
 Calculus  1. Find the area of the region bounded by the curves and lines y=e^x ...
 calculus  Find the area of region bounded by the curves y=sin(pi/2*x)and y=x^2...
 math  Find the area of the region between the curves y = sin x and y = x^2  x...
More Related Questions