1. ## Integration problems

I really dont understand this Q!

For part i) I got an answer of 0.535645, however the answer in the back of the book is 0.535644??

For part ii) i got 1 + 5x^2 + 10x^4 + 10x^6 + 5x^8 + x^10 , im pretty sure thats right however for the next bit i got an answer of 0.5826, but the actual answer is 0.527147??

Thank you so much

2. Looks like you got (i) correct.

The answer to (ii) is found by calculating

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

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

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

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

3. Originally Posted by Scott H
Looks like you got (i) correct.

The answer to (ii) is found by calculating

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

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

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

For (iv), I think you are supposed to name a few other rules besides the trapezoidal rule.
thanks a ton scott, but just wondering could you go over Q7i) again please, i did it yesterday in rough, but im trying to do it again now and i just dont seem to be getting the right answer

4. If your answer is only $0.000001$ off, then you should be fine.