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The area bounded by the curve y = tan x, X-axis and the line x = π4 is ______. - Mathematics and Statistics

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Question

The area bounded by the curve y = tan x, X-axis and the line x = `pi/(4)` is ______.

Options

  • `1/2` log 2 sq units

  • log 2 sq units

  • 2 log 2 sq units

  • 3·log 2 sq units

MCQ
Fill in the Blanks
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Solution

The area bounded by the curve y = tan x, X-axis and the line x = `pi/(4)` is `bbunderline(1/2  log  2  "sq units")`.

Explanation:

Required area = `int_0^(pi/4) tan dx`

= `log |sec x|_0^(pi/4)`

= `log sqrt2`

= `1/2` log 2 sq units.

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Area Bounded by the Curve, Axis and Line
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Chapter 5: Application of Definite Integration - Miscellaneous Exercise 5 [Page 190]

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Balbharati Mathematics and Statistics 2 (Arts and Science) [English] Standard 12 Maharashtra State Board
Chapter 5 Application of Definite Integration
Miscellaneous Exercise 5 | Q 1.17 | Page 190

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