{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Test 4a solutions

# Test 4a solutions - x is u = d-x d ` and hence the work is...

This preview shows pages 1–2. Sign up to view the full content.

Solutions for Test IV C1 I: a ) 1 5 ( x + 1) 5 - 1 4 ( x + 1) 4 + C b ) 2 5 ( x + 1) 5 / 2 - 2 3 ( x + 1) 3 / 2 + C c ) 1 3 exp( x 3 ) + C d ) 2 3 (2 3 / 2 - 1) + 2(2 1 / 2 - 1) The integral in e) vanishes since the integrand is odd. II: a) The two curves intersect at x = 0 and x = 2. hence the area is given by 2 0 ( x 2 - ( x 3 - x 2 ) ) d x = 4 3 b)The x coordinate of the centroid is determined by the integral 2 0 x ( x 2 - ( x 3 - x 2 ) ) d x = 8 5 which leads to x = 3 2 The y component of the centroid is determined by the integral 2 0 ( x 4 - ( x 3 - x 2 ) 2 ) d x which leads to y = 8 7 III: a) Denote by w = 20 the width, by = 50 the length, by d = 3 the maximal depth and by ρ = 1000 the density of water. The length of a layer of water at the depth

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: x is u = d-x d ` and hence the work is given by the integral gρ`w Z d x d-x d d x = g`wρd 2 6 = 1 . 5 × 10 7 J 1 b) The time it takes to empty the pool is 1 . 5 × 10 7 7 . 5 3 = 2000s which approximately 0 . 55 hours. IV: a) Slice parallel to the y axis. The volume is given by 2 π Z 1 x √ 1 + x d x = 4 π 15 (2 √ 2 + 1) b) Again, slice parallel to the y axis. The volume is given by the integral π Z 1 (1 + x )d x = 3 π 2 2...
View Full Document

{[ snackBarMessage ]}