Kwa wale wapenzi wa CALCULUS: tahadhari kuna maswali majibu yake yamekosewa hapa!

[Makanyaga]

Some Calculus solutions presented here (please see the PDF attachment below) are alternative corrected solutions from the Math24 website. The original solutions from the website appear as were wrongly computed using wrong limits of integration, thereby each giving a value of a region of integration as equal to zero. However, the fact is, the region of integration (be it area or volume) under any type of curve cannot be zero; it is always something bigger than zero.

The problems (and their URL) whose solutions have been corrected are as listed below

EXAMPLE 4 (Double Integrals over Rectangular Regions) (Double Integrals over Rectangular Regions - Page 2)

EXAMPLE 2 (Double Integrals in Polar Coordinates) (Double Integrals in Polar Coordinates)

EXAMPLE 3 (Double Integrals in Polar Coordinates) (Double Integrals in Polar Coordinates - Page 2)

However, where there may arise an oversight, I stand to be corrected and warmly welcome your valued contributions. Enjoy your reading



With kind regards

Makanyaga

 

[Makanyaga]

Pia kuna maswali yanaanza kwa kusema: "Calculate the double integral....". Hii nayo pia ni oversight kwenye lugha kwa sababu there is no such thing as "calculation of an integral" but rather we normally EVALUATE an integral
So the correct wording was supposed to incorporate the words:evaluate the double integral...... See an example case of the said explained discrepancy at

Change of Variables in Double Integrals which is Example 1, (Change of Variables in Double Integrals)

 

[Kunguru wa Manzese]

Write your reply...olevel bmaths-f bam-f chuo elective course ya maths sjachukua ..hapa hapaniusu .

 

[Makanyaga]

Write your reply...olevel bmaths-f bam-f chuo elective course ya maths sjachukua ..hapa hapaniusu .

Ulitakiwa kupitiliza bila kuandika kitu!

 

[Makanyaga]

Najaribu tu ku-update ili wadau waweze kuona na possibly kuto maoni yao. I need your input

 

[Makanyaga]

Some Calculus solutions presented here (please see the PDF attachment below) are alternative corrected solutions from the Math24 website. The original solutions from the website appear as were wrongly computed using wrong limits of integration, thereby each giving a value of a region of integration as equal to zero. However, the fact is, the region of integration (be it area or volume) under any type of curve cannot be zero; it is always something bigger than zero.

The problems (and their URL) whose solutions have been corrected are as listed below

EXAMPLE 4 (Double Integrals over Rectangular Regions) (Double Integrals over Rectangular Regions - Page 2)

EXAMPLE 2 (Double Integrals in Polar Coordinates) (Double Integrals in Polar Coordinates)

EXAMPLE 3 (Double Integrals in Polar Coordinates) (Double Integrals in Polar Coordinates - Page 2)

However, where there may arise an oversight, I stand to be corrected and warmly welcome your valued contributions. Enjoy your reading



With kind regards

Makanyaga

UPDATE 27/03/2020

Maswali haya tayari yameshafanyiwa marekebisho na wataalamu wa Math24 website na majibu yake kwa sasa si sifuri tena, japo yametofautiana kidogo na ya kwangu yaliyoko kwenye attachment hii niliyowahi kuitoa kipindi napost thread hii. Possibly safari hii oversight itakuwa iko kwangu, kwa sababu haiwezekani team ya wataalamu ifanye marekebisho ya maswali ambayo majibu yake yalikuwa yamekosewa, na ikosee tena majibu kwa mara ya pili, it's practically impossible.

Itabidi niangalie kuona ni wapi mimi nilikosea, halafu nitawarudishia feedback.

Mubarikiwe tena na Bwana.

With kind regards

Makanyaga

 

[Nelly]

HKL tuna comment wapi???@-

 

[Makanyaga]

HKL tuna comment wapi???@-

Nimejaribu kupitia majibu yao na nimegundua kuwa majibu yetu sote yako sahihi, ya kwao na ya kwangu pia. Sema tu safari hii walichofanya ni kwamba wamerekebisha maumbo husika, badala ya kuchukua umbile zima la swali kama lilivyokuwa mwanzo, wamechukua nusu yake, kwa maana hiyo maswali wameyarekebisha kidogo ili kuondoa ule mtafaruku wa kuwa yanaleta majibu ya sifuri. Kwa hali hiyo ukichukua majibu yao ukayazidsha kwa mbili, yanakuwa sawa na majibu yangu yaliyoko kwenye attachment yangu, au ukichkua majibu yangu ukayagawa kwa mbili, unapata majibu yao


Mugarikiwe na Bwana

 

[gasozi]

Kwahiyo ni sifuri gawia mbili eti.

Nimejaribu kupitia majibu yao na nimegundua kuwa majibu yetu sote yako sahihi, ya kwao na ya kwangu pia. Sema tu safari hii walichofanya ni kwamba wamerekebisha maumbo husika, badala ya kuchukua umbile zima la swali kama lilivyokuwa mwanzo, wamechukua nusu yake, kwa maana hiyo maswali wameyarekebisha kidogo ili kuondoa ule mtafaruku wa kuwa yanaleta majibu ya sifuri. Kwa hali hiyo ukichukua majibu yao ukayazidsha kwa mbili, yanakuwa sawa na majibu yangu yaliyoko kwenye attachment yangu, au ukichkua majibu yangu ukayagawa kwa mbili, unapata majibu yao


Mugarikiwe na Bwana
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[Makanyaga]

Kwahiyo ni sifuri gawia mbili eti.

Nimejaribu kupitia majibu yao na nimegundua kuwa majibu yetu sote yako sahihi, ya kwao na ya kwangu pia. Sema tu safari hii walichofanya ni kwamba wamerekebisha maumbo husika, badala ya kuchukua umbile zima la swali kama lilivyokuwa mwanzo, wamechukua nusu yake, kwa maana hiyo maswali wameyarekebisha kidogo ili kuondoa ule mtafaruku wa kuwa yanaleta majibu ya sifuri. Kwa hali hiyo ukichukua majibu yao ukayazidsha kwa mbili, yanakuwa sawa na majibu yangu yaliyoko kwenye attachment yangu, au ukichkua majibu yangu ukayagawa kwa mbili, unapata majibu yao


Mugarikiwe na Bwana

[/QUOTE]
Yaani kama ulikuwepo vile!