![Now is F is Continuous on an interval (..,b] then an improper integral can be define as
follow
If this limit exist , we say that Iis Convergent; if not , it is divergent](https://image.slidesharecdn.com/kenpatcalculus07-160313044735/85/IMPROPER-INTEGRAL-8-320.jpg)
![Now is F is Continuous on an interval (..,b] then an improper integral can be define as follow
If this limit exist , we say that Iis Convergent; if not , it is divergent](https://image.slidesharecdn.com/kenpatcalculus07-160313044735/85/IMPROPER-INTEGRAL-10-320.jpg)
![B) If f(x) is continuous on ( a , b]
If limit exist Integral is Converges , otherwise it is diverges.](https://image.slidesharecdn.com/kenpatcalculus07-160313044735/85/IMPROPER-INTEGRAL-13-320.jpg)
![C) If f(x) is continuous on [ a , b] and not bounded at
the point C E ( a ,b) then we can write
If limit exist Integral is Converges , otherwise it is diverges.](https://image.slidesharecdn.com/kenpatcalculus07-160313044735/85/IMPROPER-INTEGRAL-14-320.jpg)
IMPROPER INTEGRAL
- 1. Calculus
- 2. Guidance by – MAULIK PRAJAPATI Presented by KRISNADITYA RANA YATIN DESAI LAKSHMI VIMAL KISHAN PATEL SAGRIKA MAURYA SHREY PATEL 140750116048 140750111001 140750111002 140750111004 140750111003 140750111005
- 3. In most of applications of engineering and science there occurs special functions, like gamma functions ,beta functions etc , which are in the form of integrals which are of special types in which the limits of integration are infinity or the integrand becomes unbounded within the limits . Such type of integrals are known as improper integrals. Convergence of such integrals has an important and main roll rather than divergent integral . we shall discuss about the type of improper integrals
- 4. The definite integral is said to be improper integral if one or both limits of integration are infinite and/or if the integrand integral is unbounded on the interval EXAMPAL
- 5. TYPES OF INTEGRALS 1) When upper limit is infinity 2) When lower limit is infinity 3) When both limits of integration are infinity 4) When integral is Unbounded
- 6. 1) When upper limit is infinity Now is F is Continuous on an interval [a,….) then an improper integral can be define as follow If this limit exist , we say that Iis Convergent; if not , it is divergent
- 7. EXAMPAL
- 8. Now is F is Continuous on an interval (..,b] then an improper integral can be define as follow If this limit exist , we say that Iis Convergent; if not , it is divergent
- 9. EXAMPAL
- 10. Now is F is Continuous on an interval (..,b] then an improper integral can be define as follow If this limit exist , we say that Iis Convergent; if not , it is divergent
- 11. EXAMPAL
- 12. A) If f(x) is continuous on [ a , b) If limit exist Integral is Converges , otherwise it is diverges.
- 13. B) If f(x) is continuous on ( a , b] If limit exist Integral is Converges , otherwise it is diverges.
- 14. C) If f(x) is continuous on [ a , b] and not bounded at the point C E ( a ,b) then we can write If limit exist Integral is Converges , otherwise it is diverges.
- 15. Horizontal P-integral test The integral 1. Converges if P > 1 2. Diverges if P < 1_
- 16. Vertical P-integral test 1. Converges if P < 1 2. Diverges if P > 1 The integral _