Question

let f(x)=$x^{2}$+2x+1 and g(x)=2x+5. skecth the region bounded by the graphs of f(x) and g(x), and find the area of the region

Answer 1

Answer:

The area is

32/3

Start by finding the intersection points

${y=x2+2x+1 \\ y=2x+5$

$2x+5=x2+2x+1</p><p></p><p>0=x2+2x−2x+1−5</p><p></p><p>0=x2−4</p><p></p><p>0=(x+2)(x−2)</p><p></p><p>x=−2 \: and \: 2</p><p></p><p>∴y=2x+5</p><p></p><p>y=2(−2)+5 \: and \: y=2(2)+5</p><p></p><p>y=1 \: and \: y=9</p><p></p><p>$

. The next step is doing a basic sketch of the graph. This is not what I'm going to do for this answer, but this is often a necessity when you don't have access to a graphing calculator.

Answer 2

Answer:

The are is 32/3

,Hope it helps u keep smiling :)