Maharashtra State BoardHSC Commerce 12th Board Exam
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Choose the correct alternative : ∫-99x34-x2⋅dx = - Mathematics and Statistics

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MCQ

Choose the correct alternative :

`int_(-9)^9 x^3/(4 - x^2)*dx` =

Options

  • 0

  • 3

  • 9

  • – 9

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Solution

Let I = `int_(-9)^9 x^3/(4 - x^2)*dx`

Let f(x) = `x^3/(4 - x^2)`

∴ f(– x) = `(-x)^2/(4 - (-x)^2`

= `-x^3/(4 - x^2)`

= – f(x)
∴ f(x) is an odd function.

`int_(-9)^9 x^3/(4 - x^2)*dx = 0.      ...[because int_("a")^"a" f(x) = 0, if f(x) "odd function"]`

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 1.01 | Page 148
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