Evaluate ∫01 xex² dx.

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The value of the integral is (e − 1)/2. Sol'n: Let u = x², du = 2x dx → x dx = du/2 ∫ xex² dx = (1/2) ∫ eu du = (1/2)eu + C = (1/2)ex² + C Evaluate from 0 to 1: (1/2)e1 − (1/2)e0 = (e − 1)/2

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Asked 16 days ago|4/29/2026 9:48:21 AM

Updated 16 days ago|4/29/2026 4:44:11 PM

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Edited by matahari [4/29/2026 4:44:11 PM]

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Solve dx dy =y 2 with y(0)=1

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Updated 16 days ago|4/29/2026 11:07:38 AM

1 Answer/Comment

cruz30

Given: dy/dx=y^2, y(0)=1
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So -1/y = x-1
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Added 16 days ago|4/29/2026 11:07:38 AM

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Updated 16 days ago|4/29/2026 11:04:39 AM

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Added 16 days ago|4/29/2026 11:04:37 AM

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Updated 16 days ago|4/29/2026 11:18:27 AM

1 Answer/Comment

cruz30

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Added 16 days ago|4/29/2026 11:18:27 AM

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u=10, a=2, t=5 find v

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Updated 16 days ago|4/29/2026 10:19:55 AM

1 Answer/Comment

cruz30

Given: u=10, a=2, t=5
v = u + at
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Added 16 days ago|4/29/2026 10:19:55 AM

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istance with u=5, a=3, t=4

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Updated 16 days ago|4/29/2026 10:19:36 AM

1 Answer/Comment

cruz30

Given: u=5, a=3, t=4
s = ut + 1/2 a t^2
s = 5*4 + 1/2*3*4^2
s = 20 + 1.5*16
s = 20 + 24 = 44
Answer: 44 m

Added 16 days ago|4/29/2026 10:19:36 AM

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