MTH 101 Assignment # 2 Question No 1 Solution

[Ali Khawaja (7th) BSCS]

Please correct me if i am wrong

[SANA ALI]

plzzz 1 day left, send full solution of mth-101 assignment-2

[BEELOOO...]

plzz koi full solution upload kro

[Mir Ali]

aray bhai koi to kuch clear cut solution uplod kro yar suggestions ni chaiye han

proper solution bhejo dosto

kia koi bi maths ka expert nai idar??????????

[Sohail Akhtar]

Hey folks,

please note:

[f(x) - g(x)]dx

[x^2 - 3x - (-2)]

[x^2 - 3x + 2]

Please note the sign of + before 2.

[+•÷ILLUSIONIST(MCS 1st)+•÷]

ali bhai ap ne 3rd last step mein 3/4 ko 4/3 ksey kia hai aur  27/64 q likha hai plz explain

[Rabia]

x* ka kia mtlb ha i mean ye kun use kia gya ha

[SANA ALI]

plzzz 1 day left, send full solution of mth-101 assignment-2

[Mir Ali]

ye samajhne ka waqt nahi k kia kyun kese hua bs kuch rad o badal se assignment likh k bhejo sabhi

and to be honest i think koi bi confident nahi hai is sab solutions k baarey mein ajeeb bat hai koi bi mathematician nahi pooray group mein jo certainty se verify ya modify kr sake in suggestions ko so just contented rahein jo hai idar

[+•÷ILLUSIONIST(MCS 1st)+•÷]

ali raza marshal bhai agr ap mjhe thoda sa guide kr detey in points k barey main tu ju main ne pehly pochey tu apki bari inayat hoti ..... khair koe baat  nahi actually kafi bizi honey ki waja se solution mein nahi de ska.

[Ali Khawaja (7th) BSCS]

kon sa points

[+ M.Tariq Malik]

Question # 3:                                                                            Marks 5

Find the volume of the spheroid formed by the revolution of the area bounded by the ellipse  about the major axis.

Answer

By using parametric form…..

x = aCos t
y = bSin t,                    0 ≤ t ≤ π

Which gives the half ellipse with positive y

dx/dt = - aSint
dy/dt = bCos t

V = π∫(aCos t)²(bCos t) dt            on    [0,π]

Thanks to the symmetry w.r.t  y-axis we have 

V = 2πa²b∫(Cos t)²(Cos t) dt         on    [0,π/2]

    = (*)

∫(cos t)³ dt = ∫(cos t)(1 - (sin t)²) dt

Substitute 
Sin t = u
Cos t dt = du

when t = 0,          u = 0
when t = π/2,       u = 1

(*)
= 2πa²b ∫(1 - u²) du                         on     [0,1]

A primitive is:

F (u) = 2πa²b(u - (1/3) u³)

Then volume is

V = F (1) - F (0) = (4/3)πa²b

 

Hence proved.

 

[+ M.Tariq Malik]

The volume of a spheroid (of any kind) is