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.
2. Suppose that when the area A between the graph of a
function y = f(x) and an interval [a, b] is approximated by
the areas of n rectangles, the total area of the rectangles is
An = 2+ (2/n), n= 1,2,.... Then, A =,
1. Find the total area bounded by the curves y = x² − 3x and y = x³ + x² − 12x.
8. Given, h(x) = 2 – x and g(x) = -x²+ 4
a) Plot the two functions on the same graph for -2 < x <4
b) Calculate the area between the curves of h(x) and g(x) for -2
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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