Maharashtra State BoardHSC Commerce 12th Board Exam
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Fill in the blank : ∫01dx2x+5 = _______ - Mathematics and Statistics

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Fill in the Blanks

Fill in the blank : `int_0^1 dx/(2x + 5)` = _______

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Solution

Let I = `int_0^1 dx/(2x + 5)`

Put 2x + 5 = t
∴ 2dx = dt
∴ dx = `"dt"/(2)` 
When x = 0, t = 2(0) + 5 = 5
When x = 1, t = 2(1) + 5 = 7

∴ I = `(1)/(2) int_5^7 "dt"/"t"`

= `(1)/(2)[log|"t"|]_5^7`

= `(1)/(2)(log 7 - log 5)`

= `(1)/(2)log(7/5)`.

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 2.03 | Page 149
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