The integrand of the following definite integral is a difference of two functions.
Sketch the graph of the two functions and shade the region whose area is represented by the integral.

A) 1) 2)
B) 1) 2)
C) 1) 2)
D) 1) 2)
E) 1) 2)

Question

The integrand of the following definite integral is a difference of two functions. ​  ​
Sketch the graph of the two functions and shade the region whose area is represented by the integral.
​
A) ​ 1) 2) 
B) ​ 1) 2) 
C) ​ 1) 2) 
D) ​ 1) 2) 
E) ​ 1) 2)

Quizplus · Accepted Answer

The integrand is a difference of two functions, so we need to graph both functions and shade the area between them. 
For choice B, the two functions are given as $y=x^2$ and $y=2-x$. 
To graph $y=x^2$, we can use the vertex form of the equation, which gives us the vertex as $(0,0)$. We know that this is a parabola that opens upwards. 
To graph $y=2-x$, we can use the intercepts method. We can find the $y$-intercept by setting $x=0$ and the $x$-intercept by setting $y=0$. Doing this gives us $(0,2)$ and $(2,0)$, respectively. We know that this is a line with a negative slope. 
Shading the region between these two functions and finding the area gives us the value of the definite integral.

The Integrand of the Following Definite Integral Is a Difference