Finding a Region In Exercises 11-14, the integrand of the definite integral is a difference of two functions. Sketch the graph of each function and shade the region whose area is represented by the integral. ∫ − 2 1 [ ( 2 − y ) − y 2 ] d y
Finding a Region In Exercises 11-14, the integrand of the definite integral is a difference of two functions. Sketch the graph of each function and shade the region whose area is represented by the integral. ∫ − 2 1 [ ( 2 − y ) − y 2 ] d y
Solution Summary: The author analyzes the graph of each given function displaystyle 'underset' and the region to be shaded.
Finding a Region In Exercises 11-14, the integrand of the definite integral is a difference of two functions. Sketch the graph of each function and shade the region whose area is represented by the integral.
∫
−
2
1
[
(
2
−
y
)
−
y
2
]
d
y
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
Let f be a function whose graph consists of 5 line segments and a semicircle as shown in the figure below.
Let g(x) = √ƒƒ(t) dt .
0
3
2
-2
2
4
5
6
7
8
9
10
11
12
13
14
15
1. g(0) =
2. g(2) =
3. g(4) =
4. g(6) =
5. g'(3) =
6. g'(13)=
The expression 3 | (3+1/+1)
of the following integrals?
A
Ов
E
+
+
+ +
18
3+1+1
3++1
3++1
(A) √2×14 dx
x+1
(C) 1½-½√ √ ² ( 14 ) d x
(B) √31dx
(D) So 3+x
-dx
is a Riemann sum approximation of which
5
(E) 1½√√3dx
2x+1
2. Suppose the population of Wakanda t years after 2000 is given by the equation
f(t) = 45000(1.006). If this trend continues, in what year will the population reach 50,000
people? Show all your work, round your answer to two decimal places, and include units. (4
points)
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.