∫ (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?
$\displaystyle \int_0^3 (3x)^{\frac{1}{2}}+1-(x+1)\,dx$?
If so, this is the same as $\displaystyle \int_0^3 \sqrt{3}x^{\frac{1}{2}}-x\,dx$
This becomes $\displaystyle \left.\left[\frac{2\sqrt{3}}{3}x^{\frac{3}{2}}-\frac{1}{2}x^2\right]\right|_0^3=\frac{2\sqrt{3}}{3}\cdot 3\sqrt{3}-\frac{9}{2}=6-\frac{9}{2}=\frac{3}{2}=1.5$
Does this make sense?