# Calculus

posted by .

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 -

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.

## Similar Questions

1. ### Calculus (Area Between Curves)

Find the area of the region IN THE FIRST QUADRANT (upper right quadrant) bounded by the curves y=sin(x)cos(x)^2, y=2xcos(x^2) and y=4-4x. You get: a.)1.8467 b.) 0.16165 c.) 0.36974 d.) 1.7281 e.) 0.37859 Based on my calculations, I …
2. ### Calculus (Area Between Curves)

Find the area of the region IN THE FIRST QUADRANT (upper right quadrant) bounded by the curves y=sin(x)cos(x)^2, y=2xcos(x^2) and y=4-4x. You get: a.)1.8467 b.) 0.16165 c.) 0.36974 d.) 1.7281 e.) 0.37859
3. ### Calculus

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.
4. ### Calculus

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.
5. ### math

Find the area of the region between the curves y = sin x and y = x^2 - x, 0 ≤ x ≤ 2.
6. ### calculus

Find the area of region bounded by the curves y=sin(pi/2*x)and y=x^2-2x.
7. ### Calculus

1. Find the area of the region bounded by the curves and lines y=e^x sin e^x, x=0, y=0, and the curve's first positive intersection with the x-axis. 2. The area under the curve of y=1/x from x=a to x=5 is approximately 0.916 where …
8. ### Calculus-Area between curves

Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region. 2y=4*sqrt(x) , y=5 and 2y+4x=8 please help! i've been trying this problem the last couple days, even …
9. ### Calculus Area between curves

Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region. 3y+x=3 , y^2-x=1
10. ### math

Roughly sketch the region enclosed by the curves y = sin x, y = cos x and the x - axis between x = 0 and x = p/ 2 . Also find the area of this region.

More Similar Questions

Post a New Question