Integrate the following with respect to x : x(1 – x)17 - Mathematics

Question

Integrate the following with respect to x :

x(1 – x)¹⁷

Sum

Solution

`int x(1 - x)^17 "d"x`

Put 1 – x = u

– dx = du

`int x(1 - x)^17 "d"x = int (1 - "u")"u"^17 xx - "du"`

= `- int ("u"^17 - "u"^18) "du"`

= `- int "u"^17 "du" + int "u"^18 "du"`

= `- ("u"^(17 + 1))/(17 + 1) + ("u"^(18 + 1))/(18 + 1) + "c"`

= `- "u"^18/18 + "u"^19/19 + "c"`

= `- (1 - x)^18/18 + (1 - x)^19/19 + "c"`

`int x(1 - x)^17 "d"x = (1 - x)^19/19 - (1 - x)^18/18 + "c"`

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Indefinite Integration - Methods of Integration

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Q 14 Q 13 Q 15

Chapter 11: Integral Calculus - Exercise 11.6 [Page 206]

APPEARS IN

Samacheer Kalvi Mathematics - Volume 1 and 2 [English] Class 11 TN Board

Chapter 11 Integral Calculus
Exercise 11.6 | Q 14 | Page 206

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