How do you solve this integral?

**Spika** · March 2nd 2009, 07:25 PM

∫ (from 0 to 3) (((3x)^(1/2)+1) - (x+1)) dx

Can you solve it showing your work please? My professor says it's 1.5, and I can't seem to come to that. Any help would be appreciated! Thanks!

**Chris L T521** · March 2nd 2009, 08:12 PM

Originally Posted by Spika

∫ (from 0 to 3) (((3x)^(1/2)+1) - (x+1)) dx

Can you solve it showing your work please? My professor says it's 1.5, and I can't seem to come to that. Any help would be appreciated! Thanks!

Is this what you mean?

$\int_0^3 (3x)^{\frac{1}{2}}+1-(x+1)\,dx$ ?

If so, this is the same as $\int_0^3 \sqrt{3}x^{\frac{1}{2}}-x\,dx$

This becomes $\left.\left[\frac{2\sqrt{3}}{3}x^{\frac{3}{2}}-\frac{1}{2}x^2\right]\right|_0^3=\frac{2\sqrt{3}}{3}\cdot 3\sqrt{3}-\frac{9}{2}=6-\frac{9}{2}=\frac{3}{2}=1.5$

Does this make sense?

**Spika** · March 2nd 2009, 08:23 PM

Ah, thanks. I see what I was doing wrong. I was doing (3x) ^ (3/2) instead of taking the square root of 3. Thanks for the help!

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