Evaluating a Definite Integral Using a Geometric Formula In Exercises 31 and 32, sketch the region whose area is given by the definite integral. Then use a geometric I formula to evaluate the integral. ∫ 0 5 ( 5 − | x − 5 | ) d x
Evaluating a Definite Integral Using a Geometric Formula In Exercises 31 and 32, sketch the region whose area is given by the definite integral. Then use a geometric I formula to evaluate the integral. ∫ 0 5 ( 5 − | x − 5 | ) d x
Solution Summary: The graph is shown below. The area enclosed by the integral encloses a triangular region of height 5 units.
Evaluating a Definite Integral Using a Geometric Formula In Exercises 31 and 32, sketch the region whose area is given by the definite integral. Then use a geometric I formula to evaluate the integral.
∫
0
5
(
5
−
|
x
−
5
|
)
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.
1. Given the vector field F(x, y, z) = -zi, verify the relation
1
VF(0,0,0) lim
+0+ volume inside S
ff F• Nds
S.
where S, is the surface enclosing a cube centred at the origin and having edges of length 2€. Then,
determine if the origin is sink or source.
Let a = (-4, 5, 4) and 6 = (1,0, -1).
Find the angle between the vector
1) The exact angle is cos
2) The approximation in radians is
Chapter 5 Solutions
Bundle: Calculus: Early Transcendental Functions, Loose-leaf Version, 6th + WebAssign Printed Access Card for Larson/Edwards' Calculus: Early Transcendental Functions, 6th Edition, Multi-Term
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