Use the result in Exercise 31 to show that the integral
∫
C
y
z
d
x
+
x
z
d
y
+
y
x
2
d
z
is not independent of the path.
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.
Evaluate the line integral
(3ry² + 6y) dr, where C is the path traced by first moving from the
point (-3, 1) to the point (2, 1) along a straight line, then moving from the point (2, 1) to the
point (5,2) along the parabola x = y² + 1.
Sketch the domain D in the (x, y)-plane satisfying
e ≤ y ≤ 3e. In your sketch, label D and its boundaries.
≤ y ≤ 2e- and
Show that f : ℝ → ℝ, f(x) = 5x − 3 is a bijective function.
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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