problems example of intgeration by substitution

INTEGRAL COURSE

Ok friends, meet again with me, MR.Chem-eng21 in this moment mr.Chem

 will sharing about study of calculus , yeah, calculus lesson one of study that exist in chemical engineering from calculus 1 until calculus 3,,wooh, I like it. Ok, in learning calculus we must patiently and carefully.

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In calculus, integration by substitution, also known as u-substitution, is a method for finding integrals. Using thefundamental theorem of calculus often requires finding an anti derivative. For this and other reasons, integration by substitution is an important tool in mathematics. It is the counterpart to the chain rule of differentiation.

theorem A

If f is continuous then (as integral) on (a, b) and if F is any anti derivatives of f, then:

a∫bf(x)dx = F(a) − F(b)

Contoh:

Tentukan ∫2 − 1(4x − 6x2)dx

 = [2x2 − 2x3]2 − 1

 = [(2.22 − 2.23)] − [(2.22 − 2.23)] − [(2.( − 1)2 − 2.( − 1)3]

 = [(2.4 − 2.8)]-[2.1 − 2.( − 1)]

 = (8 − 16) − (2 + 2)

 =  − 8 − 4 =  − 12

Tentukan ∫8`1(x1⁄3 + x4⁄3)dx

 = ⎡⎣34.84⁄3 + 37.87⁄3⎤⎦81

 = ⎛⎝34.84⁄3 + 37.87⁄3⎞⎠ − ⎛⎝34.14⁄3 + 37.17⁄3⎞⎠

 = ⎛⎝344.16 + 37.128⎞⎠ − ⎛⎝34.1 + 37.1⎞⎠

 = ⎛⎝484 + 3847⎞⎠ − ⎛⎝34 − 37⎞⎠

 = 454 + 3817 ≈ 65, 68

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