MTH101 Quiz No. 3 File 3

Question # 1 of 10 ( Start time: 02:47:06 PM ) Total Marks: 1
Arc length of the smooth curve x=g(y) for y=a to y=b is…………………
Select correct option:
L=∫ab1+(dxdy)2−−−−−−−−√dy
L=∫ab1+(dydx)2−−−−−−−−√dx


Question # 2 of 10 ( Start time: 02:48:15 PM ) Total Marks: 1
The integral of the sum of two functions is equal to the sum of their integrals.
Select correct option:
True
False


Question # 3 of 10 ( Start time: 02:48:51 PM ) Total Marks: 1
Evaluate∫x0sintdt=
Select correct option:
1+cosx
1−cosx
1+cost
1+cost


Question # 4 of 10 ( Start time: 02:50:03 PM ) Total Marks: 1
Definite integral indicating the arc length of the curve y=x2 between x=0 and x=2 is .........
Select correct option:

L=∫021+4x2−−−−−−√dx
L=∫021+2x2−−−−−−√dx
L=∫02xdx
None of these.


Question # 5 of 10 ( Start time: 02:51:41 PM ) Total Marks: 1
Mathematically second fundamental theorem of calculus can be written as,
Select correct option:
ddx∫taf(t)dt=f/(x)
ddx∫taf(t)dt=f(x)
ddx∫taf(t)dt=f(t)
none of these


Question # 6 of 10 ( Start time: 02:53:23 PM ) Total Marks: 1
Ifthecurveover[a,b]isrevolvedabouty−axis,thenthevolumeiscalculatedbytheformula−−−−−−−
Select correct option:
∫abπ[f(x)]2dx
∫abπ[f(y)]2dy


Question # 7 of 10 ( Start time: 02:54:16 PM ) Total Marks: 1
Theareaoftheellipsex2a2+y2b2=1
Select correct option:
π(a+b)
πab
14π(a2+b2)
Noneofthese


Question # 8 of 10 ( Start time: 02:56:00 PM ) Total Marks: 1
Arc length of the curve y=1 from x=a to x=b is ............
Select correct option:
2(b-a)
b-a
a-b
0


Question # 9 of 10 ( Start time: 02:57:18 PM ) Total Marks: 1
The volume of cylindrical shell for R = 5, r = 3 and h = 2 is -----------
Select correct option:
25*pi
30*pi
32*pi
36*pi


Question # 10 of 10 ( Start time: 02:58:01 PM ) Total Marks: 1
For the adjacent intervals, [a,c] and [c,b],where c is any number,
∫baf(x)dx=
Select correct option:
∫baf(x)dx+∫acf(x)dx
∫caf(x)dx+∫bcf(x)dx
∫caf(x)dx+∫abf(x)dx
None of these