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u-substitution help (1 Viewer)

Thread starter Halo189
Start date Feb 17, 2015

Halo189

Member

Feb 17, 2015

evaluate 3 integral 0 t/sqr root (t+1) dt.

ans: 2 2/3

FrankXie

Active Member

Feb 17, 2015

$u=\sqrt{t+1}, t=u^2-1, dt=2udu, t=0, u=1; t=3, u=2, \int_0^3\frac{t}{\sqrt{t+1}}dt=\int_1^2\frac{u^2-1}{u}2udu=2\int_1^2(u^2-1)du=2\left(\frac{u^3}{3}-u\right)_1^2=\frac{8}{3}.$

Last edited: Feb 17, 2015

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