English

Evaluate : ∫19x+1x⋅dx - Mathematics and Statistics

Advertisements
Advertisements

Question

Evaluate : `int_1^9(x + 1)/sqrt(x)*dx`

Sum
Advertisements

Solution

`int_1^9(x + 1)/sqrt(x)*dx = int_1^9(x/sqrt(x) + 1/sqrt(x))*dx`

= `int_1^9 x^(1/2)*dx + int_1^9 x^(-1/2)*dx`

= `[(x^(3/2))/(3/2)]_1^9 + [(x^(1/2))/(1/2)]_1^9`

= `(2)/(3)[9^(3/2) - 1^(3/2)] + 2[9^(1/2) - 1^(1/2)]`

= `(2)/(3)[(3^2)^(3/2) - 1] + 2[3 - 1]]`

= `(2)/(3)[27 - 1] + 4`

= `(52)/(3) + 4`

= `(64)/(3)`.

shaalaa.com
  Is there an error in this question or solution?
Chapter 4: Definite Integration - Exercise 4.2 [Page 171]
Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×