A In Problems 7–16, find each antiderivative. Then use the antiderivative to evaluate the definite integral. 14. (A) ∫ ln x x y d x (B) ∫ 1 e ln x x y d x
A In Problems 7–16, find each antiderivative. Then use the antiderivative to evaluate the definite integral. 14. (A) ∫ ln x x y d x (B) ∫ 1 e ln x x y d x
Solution Summary: The author explains how to find the value of displaystyle.
AIn Problems 7–16, find each antiderivative. Then use the antiderivative to evaluate the definite integral.
14. (A)
∫
ln
x
x
y
d
x
(B)
∫
1
e
ln
x
x
y
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.
Q2. Find the points on the ellipse x²+4y² = 1, where f(x, y) = xy has its extreme value.
Q3. Find the moment of inertia about x-axis for the area bounded by the curves x = y² and
x=2y-y2 if 8 = y + 1.(20 Mark)
Q4 Find the iterated integral for the following then evaluate it: (20 Mark)
-1/√2 y2
dxdy
-1/√2 1-y2
Q8 Salve:
f√coshx-i.dx
do
Solve: So
Q₂
Qio Salve
S
Sinho + cosho
dx
4-x2
Qll Solve Sdx
√ex+1
Q12 If y = (x²+1). sech (lmx), and dy
dx
Q13 If y = /n | cschx + cothxl, Ind dy
If y = /R/cschx + cothx|, 2nd dy
3) ans.
aus.
dy: x^" [ x² + x^ (1+/nx)/nx]
dx
+
252 cosh + + C
ans.
+ 1
aims.
aims.
-2 csch'e
ans.
dy
да
= 2
12) ans.
- cschx
+ A
+ C
Chapter 7 Solutions
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
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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