Download PTU B.Sc (Non-Medical) 2020 March 2nd Sem 76303 Integral Calculus Question Paper

Download PTU (I.K. Gujral Punjab Technical University Jalandhar (IKGPTU) B.Sc (Non-Medical) 2020 March Previous Question Papers

1 | M-76303 (S105)-2583
Roll No. Total No. of Pages : 02
Total No. of Questions : 09
B.Sc (Non Medical) (2018 Batch) (Sem.?2)
INTEGRAL CALCULUS
Subject Code : BSNM-205-18
M.Code : 76303
Time : 3 Hrs. Max. Marks : 50
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying ONE mark
each.
2. SECTION-B contains FIVE questions carrying FIVE marks each and students
have to attempt any FOUR questions.
3. SECTION-C contains THREE questions carrying TEN marks each and students
have to attempt any TWO questions.

SECTION-A
1. Solve the following :
a) Find the length of the arc of the curve
3
2
y x ? from (0, 0) to (4, 8).
b) Evaluate
1 1
0 0
( 2) x dydx ?
? ?
.
c) Find the value of
1 3 2
0 0 0
dydzdx
? ? ?
.
d) Evaluate
1
( 1)
dx
x x ?
?
.
e) Evaluate
2
2
sin x dx
?
?
?
?
.
f) Show that
6
7
0
16
sin 3
105
x dx
?
?
?
.
g) Evaluate
2 x
x e dx
?
.
h) Prove that ( ) ( ) f y dx f y dx
? ?
? ?
? ?
? ?
.
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1 | M-76303 (S105)-2583
Roll No. Total No. of Pages : 02
Total No. of Questions : 09
B.Sc (Non Medical) (2018 Batch) (Sem.?2)
INTEGRAL CALCULUS
Subject Code : BSNM-205-18
M.Code : 76303
Time : 3 Hrs. Max. Marks : 50
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying ONE mark
each.
2. SECTION-B contains FIVE questions carrying FIVE marks each and students
have to attempt any FOUR questions.
3. SECTION-C contains THREE questions carrying TEN marks each and students
have to attempt any TWO questions.

SECTION-A
1. Solve the following :
a) Find the length of the arc of the curve
3
2
y x ? from (0, 0) to (4, 8).
b) Evaluate
1 1
0 0
( 2) x dydx ?
? ?
.
c) Find the value of
1 3 2
0 0 0
dydzdx
? ? ?
.
d) Evaluate
1
( 1)
dx
x x ?
?
.
e) Evaluate
2
2
sin x dx
?
?
?
?
.
f) Show that
6
7
0
16
sin 3
105
x dx
?
?
?
.
g) Evaluate
2 x
x e dx
?
.
h) Prove that ( ) ( ) f y dx f y dx
? ?
? ?
? ?
? ?
.
2 | M-76303 (S105)-2583
i) Evaluate
3
2 2
2
( )
dx
a x ?
?
.
j) Write the formula for the volume of the solid generated by the revolution about the x-
axis, of the area bounded by the curves y = f (x), y = g (x), and the ordinates x = a, x =
b.

SECTION-B
2. Evaluate
1
sin x dx
?
?
.
3. Find the volume of the spindle shaped solid generated by revolving the asteroid
2 2 2
3 3 3
x y a ? ? axis the x-axis.
4. Find the area bounded by the curves y
2
= 4ax and x
2
= 4ay.
5. Evaluate
2
1
2
1
cosh , | | 1
1
x
dx x
x
?
? ?
?
?
? ?
? ?
?
? ?
?
.
6. Evaluate
2
0
logsin x dx
?
?
.

SECTION-C
7. If
2
0
sin , 1
n
n
U x x dx n
?
? ?
?
. Prove that U
n
+ n (n ? 1) U
n?2
= n
1
2
n ?
? ? ?
? ?
? ?
. Hence find the value
of U
5
.
8. Find the volume of a right circular cylinder with base radius r and height h.
9. a) Evaluate
1 1
2
0
sin
x
y
? ?
dydx by changing the order of integration.
b) Evaluate
2 2
( )
R
x y dxdy ?
? ?
where R is the region bounded by the four hyperbolas
x
2
? y
2
= 2, 9 and xy = 2, 4.

NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any
page of Answer Sheet will lead to UMC against the Student.
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