U Substitution (a) State the Substitution Rule. Explain its connection to the Chain Rul- (b) Evaluate the indefinite integrals by using the suggested substitutions i. ii. iii. S 6x cos(x²) dx, sin(6x) cos(6x) -dx, u = x² u = cos(6x) [²√³ u = x5 + 11 X x5 + 11dx,

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Solve a) i.Evaluate using u substitution.

2. U Substitution
(a) State the Substitution Rule. Explain its connection to the Chain Rule.
(b) Evaluate the indefinite integrals by using the suggested substitutions.
i.
ii.
iii.
[61
1
6x cos(x²) dx,
sin (6x)
cos(6x)
J
dx,
U = x²
fa
[x²√x³
u = x5 + 11
X
(c) Evaluate the indefinite integrals by selection an appropriate substitu
definito integralsh
x5 + 11dx,
u = cos(6x)
Transcribed Image Text:2. U Substitution (a) State the Substitution Rule. Explain its connection to the Chain Rule. (b) Evaluate the indefinite integrals by using the suggested substitutions. i. ii. iii. [61 1 6x cos(x²) dx, sin (6x) cos(6x) J dx, U = x² fa [x²√x³ u = x5 + 11 X (c) Evaluate the indefinite integrals by selection an appropriate substitu definito integralsh x5 + 11dx, u = cos(6x)
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