gemouljr
06.05.2020 •
Mathematics
What is the area of the region between the graphs of f(x) = x^2 + 2xf(x) = x2 +2x, and g(x) = 2x+1g(x) = 2x+1g(x) = 2x + 1?
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Ответ:
enclosed area A = 2/3 units^2
Step-by-step explanation:
Given:-
- The two functions are given:-
f ( x ) = x^2 + 2x
g ( x ) = 2x + 1
Find:-
What is the area of the region between the graphs of f(x) and g(x)
Solution:-
- We will determine the interval or limits in which the two given function f(x) and g(x).
- We will find the interval by determining the point of intersection between the two graphs. Hence,
f ( x ) = g ( x )
x^2 + 2x = 2x + 1
x^2 = 1
x = ± 1 , y = 3 , -1
- The pair of intersection coordinates are ( -1 , -1 ) and ( 1 , 3 ). The functions are bounded by the intervals:
-1 ≤ x ≤ 1
-1 ≤ y ≤ 3
- Now sketch each function to visualize the enclosed region. ( See attachment ). We see that in the range ( -1 ≤ x ≤ 1 ) the function g ( x ) > f ( x ).
- So we will find the area along the y-direction with the interval ( -1 ≤ x ≤ 1 ) will define the limits of integration. The enclosed area is given by:
- The limits of integration are [ a , b ] = [ 1 , -1 ].
- The enclosed area A = 2/3 units^2.
Ответ:
(x+9)(x-7)
Step-by-step explanation:
hope it helps