Originally Posted by

**Scott H** Looks like you got (i) correct.

The answer to (ii) is found by calculating

$\displaystyle \int_0^{0.4} (1+5x^2+10x^4)\,dx=\left[x+\frac{5}{3}x^2+2x^5\right]_0^{0.4}=0.4+\frac{5}{3}\cdot 0.064+2\cdot 0.01024.$

For (iii), we look at the graph and decide whether the total area of trapezoids drawn with endpoints on the curve is greater or less than the actual area under the curve. Also, we may note that

$\displaystyle 1+5x^2+10x^4\le 1+5x^2+10x^4+10x^6+5x^8+x^{10}.$

For (iv), I think you are supposed to name a few other rules besides the trapezoidal rule.