Converting the Limits of Integration In Exercises 37-42, Evaluate the definite integral using (a) The given integration limits and (b) The limits obtained by Trigonometric Substitution. ∫ 4 6 x 2 x 2 − 9 d x .
Converting the Limits of Integration In Exercises 37-42, Evaluate the definite integral using (a) The given integration limits and (b) The limits obtained by Trigonometric Substitution. ∫ 4 6 x 2 x 2 − 9 d x .
Solution Summary: The author calculates the value of the given definite integral by using the trigonometric substitution x=amathrmsectheta.
Converting the Limits of Integration In Exercises 37-42, Evaluate the definite integral using
(a) The given integration limits and (b) The limits obtained by Trigonometric Substitution.
∫
4
6
x
2
x
2
−
9
d
x
.
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.
Finding an Indefinite Integral In Exercises
9–30, find the indefinite integral and check the
result by differentiation.
x(5x2 + 4)° dx
15.
16.
x?
;dx
(1 + x³)?
6x?
23.
24.
dx
(4x3 – 9)3
-
Applications of Integral Calculus:
Physically, integrating f(xr)dx
means finding the
area under the curve from a to b
(A)
(B)
area to the left of point a
area to the right of point b
(C)
(D)
area above the curve froma to b
Uく 0
0 0 0 0
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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