Evaluate each integral. Then state whether the result indicates that there is more area above or below the x -axis or that areas above and below the axis are equal. ∫ − 1 1 ( x 3 − 3 x ) d x
Evaluate each integral. Then state whether the result indicates that there is more area above or below the x -axis or that areas above and below the axis are equal. ∫ − 1 1 ( x 3 − 3 x ) d x
Solution Summary: The author explains the formula of definite integral to calculate the value of the given integral.
Evaluate each integral. Then state whether the result indicates that there is more area above or below the x-axis or that areas above and below the axis are equal.
∫
−
1
1
(
x
3
−
3
x
)
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.
5
Use the method of disks to find the volume of the solid that is obtained
when the region under the curve y = over the interval [4,17] is rotated
about the x-axis.
3. Use the method of washers to find the volume of the solid that is obtained
when the region between the graphs f(x) = √√2 and g(x) = secx over the
interval ≤x≤ is rotated about the x-axis.
4. Use cylindrical shells to find the volume of the solid generated when the
region enclosed by the given curves is revolved about the x-axis.
y = √√x, y = 0, y = √√3
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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