Maharashtra State BoardHSC Commerce 12th Board Exam
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Solve the following : ∫13x2logx⋅dx - Mathematics and Statistics

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Sum

Solve the following : `int_1^3 x^2 log x*dx`

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Solution

Let I = `int_1^3 x^2 log x*dx`

= `[log x int x^2*dx]_1^3 - int_1^3 [d/dx (log x) int x^2*dx]*dx`

= `[log x* x^3/3]_1^3 - int_1^3 (1)/x* x^3/(3) *dx`

= `[9 log 3 - log 1* 1/3] - (1)/(3) int_1^3 x^2*dx`

= `[9 log 3 - 0] - (1)/(3)[x^3/3]_1^3`

= `9 log 3 - (1)/(3)(27/3 - 1/3)`

= `9 log 3 - (1)/(3)(26/3)`

∴ I = `9 log 3 - (26)/(9)`.

Concept: Fundamental Theorem of Integral Calculus
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APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 6 Definite Integration
Miscellaneous Exercise 6 | Q 4.03 | Page 150
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