Question

Decide whether the given integral converges or diverges. +∞o 3 dx converges diverges If.the.integral converges, compute its value. (If the integral diverges, enter DNE.) Enter an exact number. x1.5

Answer

 ANSWER 

Converges

its value is  .

 EXPLANATION

+00 3 dx X1.5
= 3 /+00 x-1.5 dx
=3\lim_{s\rightarrow \infty}\int_{1}^{s}x^{-1.5}dx

= 3 lim $→∞0 X-1.5+1 (-1.5+1). S   (Using power rule of integration : Jx₁ | xdx : n+1 n+1)

= 3 lim xo+s -0.5 X (-0.5) 35 S
1 = -6 lim $-+x0X0.5 S
= -6 lim $+00 1 $0.5 1 10.5
=-6\lim_{s\rightarrow \infty}\left [ \frac{1}{s^{0.5}} -1\right ]
= -6 lim $+x0 1 $0.5 +6

9+0.9-=    (Since, s\rightarrow \infty , 0+ S then, 1 $0.5 0+)

=6

Since the integral is finite, it converges  and its value is 6.

  1. Education Tags
  2. :
    • Homework help
    • Study resources
    • Academic assistance
    • Le
    • arning materials
    • Educational support
    • Online tutoring
    • Study guides
    • Exam preparation
    • Homework solutions
    • School assignments
  3. Subject-specific Tags:
    • Mathematics
    • Science
    • English/Language Arts
    • History
    • Geography
    • Computer Science
    • Economics
    • Psychology
    • Sociology
    • Literature
  4. Grade Level Tags:
    • Elementary school
    • Middle school
    • High school
    • College
    • University
    • Graduate level
    • K-12
  5. Study Tools Tags:
    • Practice problems
    • Worksheets
    • Flashcards
    • Quiz questions
    • Lecture notes
    • Textbook solutions
    • Study tips
    • Exam strategies
  6. Online Learning Tags:
    • E-learning
    • Distance education
    • Virtual classroom
    • Online courses
    • Digital learning
    • Remote learning
    • Internet resources
  7. Additional Tags:
    • Free answers
    • Homework assistance
    • Academic resources
    • Study community
    • Student help
    • Assignment help
    • Problem-solving
    • Tutoring services
    • Peer collaboration
  8. Chegg Unlock
    • Chegg free questions
    • Chegg Answers
    • Bartleby Answers
    • CourseHero unlock
  9. Mail us or contact us if you need any help related to your homework and assignments. Also, for the projects as well.

Leave a Reply

Discover more from Technical Gamer

Subscribe now to keep reading and get access to the full archive.

Continue reading