In Problems 27–32, graph the region R bounded by the graphs of the indicated equations. Describe R in set notation with double inequalities, and evaluate the indicated integral. 29. y = 4 x − x 2 , y = 0 ; ∬ R y + x 2 d A
In Problems 27–32, graph the region R bounded by the graphs of the indicated equations. Describe R in set notation with double inequalities, and evaluate the indicated integral. 29. y = 4 x − x 2 , y = 0 ; ∬ R y + x 2 d A
In Problems 27–32, graph the region R bounded by the graphs of the indicated equations. Describe R in set notation with double inequalities, and evaluate the indicated integral.
29.
y
=
4
x
−
x
2
,
y
=
0
;
∬
R
y
+
x
2
d
A
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.
1. Let y = x² + 1 and y = −2x + 1.
(a) Graph the two functions together on the same plane. Find the points of intersection.
(b) Find the area of the region bounded by the line z = −2 on the left, the line x = 2
on the right, and the graphs of the functions y = x² + 1 and y = −2x + 1.
5. Find the dimensions of the largest rectangle(area-wise) which can be inscribed in the
region bounded by the x-axis, the y-axis, and the graph of y=8-x'
1. Find the total area bounded by the curves y = x² − 3x and y = x³ + x² − 12x.
Chapter 7 Solutions
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Definite Integral Calculus Examples, Integration - Basic Introduction, Practice Problems; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=rCWOdfQ3cwQ;License: Standard YouTube License, CC-BY