Hi,
Can someone please help me with the two questions attached?
thanksssss
\[ \text{Since you have the sketch of the cubic given you know your integration boundaries.}\\ \text{To do the integral, you can just expand the brackets to get}\\ y=x (-x^2+5x-6) \implies \boxed{y = -x^3+5x^2-6x} \]
\begin{align*}\therefore A&= \left| \int_0^2 -x^3+5x^2-6x\, dx \right| + \int_2^3 -x^3+5x^2-6x\,dx \end{align*}
\[ \text{The rest is left as your exercise to compute.} \]
With regards to the second question, it technically is not a part of the 2U course. However some textbooks teach the rule \( \int f^\prime(x) e^{f(x)}dx = e^{f(x)}+C\) anyway. If your textbook does this, you should consider the fact that \( \int (x^2+1)e^{x^3+3x}dx = \frac13 \int (3x^2+3)e^{x^3+3x}dx \), and try applying the formula from there.
hey! please help...
evaluate:
bounds 2 and 1 for 2x^3-x^2+5x+3 all over x, dx
I don't see where the main difficulty is in this question. Please post relevant working out or add specifically where the problem is.