Integration
Menu
Question 2
(i)
Find $\frac{\text{d}}{\text{d}t}\left[ \frac{1}{5}{{\left( 2t+1 \right)}^{\frac{5}{2}}}-\frac{1}{3}{{\left( 2t+1 \right)}^{\frac{3}{2}}} \right]$.
(ii)
Hence or otherwise, find $\int{t\sqrt{2t+1}}\,\text{d}t$.
(i)
(ii)
Question 3
Given that $\frac{{{\text{d}}^{2}}y}{\text{d}{{x}^{2}}}=2x-1$ and that $\frac{\text{d}y}{\text{d}x}=6$ when $x=2$, find the increase in $y$ when $x$ increases from $2$ to $3$.
