A In Problems 7–16, find each antiderivative. Then use the antiderivative to evaluate the definite integral. 7. (A) ∫ 12 x 2 y 3 d y (B) ∫ 0 1 12 x 2 y 3 d y
A In Problems 7–16, find each antiderivative. Then use the antiderivative to evaluate the definite integral. 7. (A) ∫ 12 x 2 y 3 d y (B) ∫ 0 1 12 x 2 y 3 d y
Solution Summary: The author explains how to find the anti-derivative of displaystyle, which is 3x2y4+c.
AIn Problems 7–16, find each antiderivative. Then use the antiderivative to evaluate the definite integral.
7. (A)
∫
12
x
2
y
3
d
y
(B)
∫
0
1
12
x
2
y
3
d
y
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. Find the antiderivative of the function
4x3 - 2x2 + x -5 dx
. Eliminate the constant 'a' from the equation
(x - a)2 + y? = a²
O (x? - 2y)dx + 2rydy = 0
O (x? - y?)dx + 2xydy = 0
1/3 + 4y/6 = 2/3
Show your work
Chapter 7 Solutions
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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