# CALCULUS

Sketch the region enclosed by the given curves.
y = 4/X
y = 16x, y = 1X/16
x > 0
and the area between the curves

1. 👍 0
2. 👎 0
3. 👁 4,986
1. Can you sketch the curves?

1. 👍 0
2. 👎 0
👨‍🏫
bobpursley
2. yes i just need the area i didn't know how to sketch it on here

1. 👍 0
2. 👎 0
3. If I read it correctly, you have
y=4/x, y=16x, and y=x/16 for x>0

You need to break the area into two regions, because the two top curves intersect at x = 1/2

So the area is

∫[0,1/2] 16x - x/16 dx + ∫[1/2,8] 4/x - x/16 dx
= (8x^2-x^2/32)[0,1/2] + (4logx-x^2/32)[1/2,8]
= 255/128 + (4log16 - 255/128)
= 4log16 = 16log2

1. 👍 4
2. 👎 4
4. thank you!

1. 👍 0
2. 👎 0
5. or that's not right

1. 👍 0
2. 👎 0
6. change the 16log(2) to 16ln(2) and then the answer is correct.

1. 👍 4
2. 👎 1
7. excellent! thanks a lot!

1. 👍 1
2. 👎 0

## Similar Questions

1. ### 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,

2. ### Calculus

Sketch the region enclosed by the curves given below. Decide whether to integrate with respect to x or y. Then find the area of the region. y=4cos(x),y=4−8x/π. I thought it was the integral of 4cos(x)- the integral of 4- 8x/π

3. ### math

Sketch the region enclosed by the given curves. y = 4/x, y = 16x, y =1/4x, x > 0 Find the area.

4. ### CALCULUS

Sketch the region enclosed by the given curves. y = tan 3x, y = 2 sin 3x, −π/9 ≤ x ≤ π/9 then then find the area. i can sketch but cant find correct area

1. ### calculus

Sketch the region enclosed by the curves x=64−y^2 and x=y^2−64. Decide whether to integrate with respect to x or y. Then find the area of the region. Area =

2. ### calculus

Consider the solid obtained by rotating the region bounded by the given curves about the x-axis. y = 9 - 9x^2 , y = 0 Find the volume V of this solid. Sketch the region, the solid, and a typical disk or washer. Any help or tips

3. ### calculus

Sketch the region in the first quadrant enclosed by y=6/x, y=2x, and y=12x. Decide whether to integrate with respect to x or y. Then find the area of the region.

4. ### Calculus

Sketch the region enclosed by the curves x= 49-y^2 and x = y^2 - 49. Decide whether to integrate with respect to x or y. Then find the area of the region.

1. ### Calculus II

Sketch the region enclosed by 2y=5x^(1/2), y=3, 2y+4x=9. Decide whether to integrate with respect to x or y, and then find the area of the region.

2. ### MATH -CALCULUS

SKETCH THE REGION ENCLOSED BY THE GIVEN CURVES: Y=|10X|, Y=X^2-11

3. ### calculus

Sketch the region enclosed by 2y=5sqrtx, y=5 and 2y+3x=8. Decide whether to integrate with respect to x or y, and then find the area of the region.

4. ### calculus

Sketch the region in the first quadrant enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region. y=10cosx, y=10sin2x,x=0