# Integrate the following with respect to the respective variable : (x-2)2x - Mathematics and Statistics

Sum

Integrate the following with respect to the respective variable : (x - 2)^2sqrt(x)

#### Solution

Let I = int (x - 2)^2 sqrt(x)*dx

= int (x^2 - 4x + 4)sqrt(x)*dx

= int (x^(5/2) - 4x^(3/2) + 4x^(1/2))*dx

= int x^(5/2)*dx - 4 int x^(3/2)*dx + 4 int x^(1/2)*dx

= x^(7/2)/((7/2)) - 4 x^(5/2)/((5/2)) + 4 x^(3/2)/((3/2))

= (2)/(7)x^(7/2) - 8x^(5/2) + (8)/(3)x^(3/2) + c.

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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board
Chapter 3 Indefinite Integration
Miscellaneous Exercise 3 | Q 2.1 | Page 150