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 illustrates the integral's shaded region, which lies between y=-2to 1.
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.
Use the information to find and compare Δy and dy. (Round your answers to four decimal places.)
y = x4 + 7 x = −3 Δx = dx = 0.01
Δy =
dy =
4. A car travels in a straight line for one hour. Its velocity, v, in miles per hour at six minute intervals is shown
in the table. For each problem, approximate the distance the car traveled (in miles) using the given method,
on the provided interval, and with the given number of rectangles or trapezoids, n.
Time (min) 0 6 12 18|24|30|36|42|48|54|60
Speed (mph) 0 10 20 40 60 50 40 30 40 40 65
a.) Left Rectangles, [0, 30] n=5
b.) Right Rectangles, [24, 42] n=3
c.) Midpoint Rectangles, [24, 60] n=3
d.) Trapezoids, [0, 24] n=4
The bracket BCD is hinged at C and attached to a control cable at B. Let F₁ = 275 N and F2 = 275 N.
F1
B
a=0.18 m
C
A
0.4 m
-0.4 m-
0.24 m
Determine the reaction at C.
The reaction at C
N Z
F2
D
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