Integrals of Functions Involving Absolute Values In Exercises 45–52, use integration by parts to evaluate the given integral using the following integral formulas where necessary. (You have seen some of these before; all can be checked by differentiating.) Integral Formula Shortcut Version ∫ | x | x d x = | x | + C Because d d x | x | = | x | x ∫ | a x + b | a x + b d x = 1 a | a x + b | + C ∫ | x | d x = 1 2 x | x | + C ∫ | a x + b | d x = 1 2 a ( a x + b ) | a x + b | + C ∫ x | x | d x = 1 3 x 2 | x | + C ∫ ( a x + b ) | a x + b | d x = 1 3 a ( a x + b ) 2 | a x + b | + C ∫ x 2 | x | d x = 1 4 x 3 | x | + C ∫ ( a x + b ) 2 | a x + b | d x = 1 4 a ( a x + b ) 3 | a x + b | + C ∫ 3 x | x + 4 | x + 4 d x
Integrals of Functions Involving Absolute Values In Exercises 45–52, use integration by parts to evaluate the given integral using the following integral formulas where necessary. (You have seen some of these before; all can be checked by differentiating.) Integral Formula Shortcut Version ∫ | x | x d x = | x | + C Because d d x | x | = | x | x ∫ | a x + b | a x + b d x = 1 a | a x + b | + C ∫ | x | d x = 1 2 x | x | + C ∫ | a x + b | d x = 1 2 a ( a x + b ) | a x + b | + C ∫ x | x | d x = 1 3 x 2 | x | + C ∫ ( a x + b ) | a x + b | d x = 1 3 a ( a x + b ) 2 | a x + b | + C ∫ x 2 | x | d x = 1 4 x 3 | x | + C ∫ ( a x + b ) 2 | a x + b | d x = 1 4 a ( a x + b ) 3 | a x + b | + C ∫ 3 x | x + 4 | x + 4 d x
Solution Summary: The author explains how to calculate the value of integral displaystyleint 3xleft|x+4right|x + 4dx
Integrals of Functions Involving Absolute Values In Exercises 45–52, use integration by parts to evaluate the given integral using the following integral formulas where necessary. (You have seen some of these before; all can be checked by differentiating.)
Integral Formula
Shortcut Version
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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.
a
->
f(x) = f(x) = [x] show that whether f is continuous function or not(by using theorem)
Muslim_maths
Use Green's Theorem to evaluate F. dr, where
F = (√+4y, 2x + √√)
and C consists of the arc of the curve y = 4x - x² from (0,0) to (4,0) and the line segment from (4,0) to
(0,0).
Evaluate
F. dr where F(x, y, z) = (2yz cos(xyz), 2xzcos(xyz), 2xy cos(xyz)) and C is the line
π 1
1
segment starting at the point (8,
'
and ending at the point (3,
2
3'6
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