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IITM BS Week 9 Mathematics 1 Questions | Prasnya
Mathematics 1 > Week 9
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13Q
01
Let
f
(
x
)
=
28
x
2
+
1
2
f(x) = 28x^2 + \frac{1}{2}
f
(
x
)
=
28
x
2
+
2
1
,
0
≤
x
≤
6
0 \le x \le 6
0
≤
x
≤
6
. The estimated area obtained by dividing the interval into
3
3
3
sub-intervals of equal length and using the left end points of the sub-intervals for height of the rectangles is (in square units):
Numerical
MEDIUM
5 marks
10 May 2026
02
Consider the function
f
(
x
)
=
x
−
4
x
f(x) = x - \frac{4}{x}
f
(
x
)
=
x
−
x
4
on the interval
[
2
,
8
]
[2, 8]
[
2
,
8
]
. Approximate the value of
∫
2
8
3
f
(
x
)
d
x
\int_2^8 3f(x) \, dx
∫
2
8
3
f
(
x
)
d
x
using the right hand Riemann sum by taking
3
3
3
sub-intervals of equal length.
Numerical
MEDIUM
4 marks
21 December 2025
03
Find the area of the region bounded by the function
f
(
x
)
=
3
x
1
−
x
2
f(x) = 3x\sqrt{1 - x^2}
f
(
x
)
=
3
x
1
−
x
2
and the lines
x
=
0
x = 0
x
=
0
,
x
=
1
x = 1
x
=
1
, and
y
=
0
y = 0
y
=
0
.
Numerical
MEDIUM
4 marks
22 December 2024
04
If
A
A
A
and
B
B
B
are the areas under the curves
v
(
t
)
v(t)
v
(
t
)
and
s
(
t
)
s(t)
s
(
t
)
respectively, from
t
=
0
t = 0
t
=
0
to
t
=
1
t = 1
t
=
1
, then what is the value of
[
A
]
+
[
B
]
[A] + [B]
[
A
]
+
[
B
]
?
Comprehension
MEDIUM
3 marks
01 September 2024
05
Is this statement True or False: The area under the curve bounded by
f
1
(
x
)
f_1(x)
f
1
(
x
)
in the interval
[
0
,
2
]
[0, 2]
[
0
,
2
]
is
8
/
3
8/3
8/3
.
Comprehension
EASY
1 marks
24 December 2023
06
Is this statement True or False: The difference in savings of Srikanth and Subendu is
2
/
3
2/3
2/3
.
Comprehension
MEDIUM
1 marks
24 December 2023
07
Is this statement True or False: The absolute error in the prediction of savings of Subendu is
4
/
3
4/3
4/3
.
Comprehension
MEDIUM
1 marks
24 December 2023
08
Find the value of
∫
0
π
/
2
f
(
x
)
d
x
\int_0^{\pi/2} f(x) \, dx
∫
0
π
/2
f
(
x
)
d
x
.
Comprehension
EASY
1 marks
24 December 2023
09
Consider the function
f
(
x
)
=
x
−
4
x
f(x) = x - \frac{4}{x}
f
(
x
)
=
x
−
x
4
on the interval
[
2
,
8
]
[2, 8]
[
2
,
8
]
. Approximate the value of
∫
2
8
3
f
(
x
)
d
x
\int_2^8 3f(x) \, dx
∫
2
8
3
f
(
x
)
d
x
using the right hand Riemann sum by taking 3 sub-intervals of equal length.
Numerical
MEDIUM
3 marks
11 December 2022
10
Find the value of the given definite integral:
∫
1
∞
ln
(
x
)
x
2
d
x
\int_1^\infty \frac{\ln(x)}{x^2} \, dx
∫
1
∞
x
2
ln
(
x
)
d
x
Numerical
MEDIUM
4 marks
11 December 2022
11
If the estimated area
A
A
A
of the region bounded by the graph of the function
f
(
x
)
=
x
2
+
1
f(x) = x^2 + 1
f
(
x
)
=
x
2
+
1
above the interval
[
1
,
4
]
[1,4]
[
1
,
4
]
using the trapezoidal Riemann sum, by taking 3 subintervals of equal length. Find the value of
2
A
2A
2
A
.
Numerical
MEDIUM
3 marks
07 August 2022
12
Find the value of
∫
−
π
π
(
x
+
sin
(
π
x
)
)
d
x
\int_{-\pi}^{\pi} (x + \sin(\pi x)) \, dx
∫
−
π
π
(
x
+
sin
(
π
x
))
d
x
.
Comprehension
EASY
2 marks
07 August 2022
13
Find the value of
∫
0
1
/
2
8
x
e
2
x
d
x
\int_{0}^{1/2} 8x e^{2x} \, dx
∫
0
1/2
8
x
e
2
x
d
x
.
Comprehension
MEDIUM
3 marks
07 August 2022
Showing 13 questions.
Complete question index for this section:
Question 1 (integer):
Question 2 (integer):
Question 3 (integer):
Question 4 (comprehension):
Question 5 (comprehension):
Question 6 (comprehension):
Question 7 (comprehension):
Question 8 (comprehension):
Question 9 (integer):
Question 10 (integer):
Question 11 (integer):
Question 12 (comprehension):
Question 13 (comprehension):
