Evaluate ∫13logx dx - Mathematics and Statistics

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Sum

Evaluate `int_1^3 log x  "d"x`

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Solution

Let I = `int_1^3 log x  "d"x`

= `int_1^3 logx*1  "d"x`

= `[log x int 1*"d"x]_1^3 - int_1^3["d"/("d"x) (log x) int1*"d"x]  "d"x`

= `[logx*(x)]_1^3 - int_1^3 1/x*x  "d"x`

= `[x log x]_1^3 - int_1^3 1*"d"x`

= (3 log 3 – 1 log 1) – `[x]_1^3`

= (3 log 3 – 0) – (3 – 1)

= 3 log 3 – 2

= log 33 – 2

∴ I = log 27 – 2

Concept: Fundamental Theorem of Integral Calculus
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Chapter 1.6: Definite Integration - Q.5

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