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  1. 12.8
  2. 14
  3. 7
  4. 12.4

Answer (Detailed Solution Below)

Option 4 : 12.4
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Detailed Solution

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Concept:

Integration of Algebraic Functions:

  • The given integral is a definite integral involving powers of x.
  • We simplify the expression using the identity: √x = x1/2.
  • Use the rule: , where n ≠ −1.
  • For definite integrals, apply the limits after integration:

 

Calculation:

Given,

⇒ x × √x = x × x1/2 = x3/2

⇒

⇒

⇒

⇒

⇒ 45/2 = (√4)5 = 25 = 32

⇒ 15/2 = 1

⇒  = 12.4

∴ The value of the definite integral is 12.4

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Latest Army Havildar SAC Updates

Last updated on Jul 1, 2025

-> The Indian Army has released the Exam Date for Indian Army Havildar SAC (Surveyor Automated Cartographer).

->The Exam will be held on 9th July 2025.

-> Interested candidates had applied online from 13th March to 25th April 2025.

-> Candidates within the age of 25 years having specific education qualifications are eligible to apply for the exam.

-> The candidates must go through the Indian Army Havildar SAC Eligibility Criteria to know about the required qualification in detail. 

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