Hi im stuck on 3 questions from my maths txt book.
questions 7,11, and 12
answers are
7: 0.41
11: 0.94
12: 0.92
my answer for 7 comes up as 5.75, 11 and 12 are off aswell.
thx in advance all help is appreciated.
I'll show you how to do #7. The following questions can be done by the same method:
$\displaystyle \int_0^2 \left(\frac1{x+4}\right) dx$ is to be approximated by 2 stripes:
1. Divide the interval [0, 2] into 2 equal parts: [0, 1], (1, 2]. The length of each part is 1.
2. Calculate
$\displaystyle f(0) = \frac14$
$\displaystyle f(1) = \frac15$
$\displaystyle f(2) = \frac16$
3. Calculate the area of the 2 trapezoids:
$\displaystyle
\frac{\frac14 + \frac15}{2} \cdot 1 +
\frac{\frac15 + \frac16}{2} \cdot 1 = \frac18 + \frac15 + \frac1{12} = \frac{49}{120} \approx 0.4083...$ Since the upper border of the trapezoids is allways above the curve this value must be slightly too large.
4. The exact value is
$\displaystyle \int_0^2 \left(\frac1{x+4}\right) dx = \left. \ln(x+4) \right|_0^2 = \ln(6) - \ln(4) = \ln\left(\frac32\right) \approx 0.405...$
sweet thx , these are just a breeze now
i needed to check were im rushing figured out 11. working on 12 now
F(1)=1
F(2)=1/4
F(3)=1/9
F(4)=1/16
F(5)=1/25
h=5-1/4 = 1
1/2((1+1/25)+2(1/4 +1/9+1/16))
= 0.9436....
thx alot they dont seem much of a challenge now.