Integral Calculus Exam Questions and Correct Answers Latest Update 2024 (Already Passed)
Find the total length of the curve r = 4(1 - Sinθ) from θ = 90° to θ = 270° and also the total perimeter of
the curve.
a. 12, 24
b. 15, 30
c. 16, 32
d. 18, 36 - Answers C
Find the length of the curve r = 4Sin θ from θ = 0° to θ = 90° and also the total length of curve.
a. π ; 2π
b. 2π ; 4π
c. 3π ; 6π
d. 4π ; 8π - Answers B
Find the length of the curve r = a (1 - Cosθ) from θ = 0° to θ = π and also the total length of the curve.
a. 2a ; 4a
b. 3a ; 6a
c. 4a ; 8a
d. 5a ; 9a - Answers C
Find the total length of the curve r = a Cosθ.
a. πa
b. 2πa
c. 1.5πav
d. 0.67πa - Answers A
,Find the length of the curve having a parametric equations of x = a Cos3θ, y = a Sin2θ from θ = 0° to θ =
2π.
a. 5a
b. 6a
c. 7a
d. 8a - Answers B
Find the centroid of the area bounded by the curve y = 4 - x2, the line x = 1 and the coordinate axes.
a. (0.24, 1.57)
b. (1.22, 0.46)
c. (0.48, 1.85)
d. (2.16, 0.53) - Answers C
Find the centroid of the area under y = 4 - x2 in the first quadrant.
a. (0.75, 1.6)
b. (1.6, 0.95)
c. (0.74, 1.97)
d. (3.16, 2.53) - Answers A
Find the centroid of the area in first quadrant bounded by the curve y2 = 4ax and the latus rectum.
a. (0.6a, 0.75a)
b. (1.23a, 0.95a)
c. (0.94a, 2.97a)
d. (1.16a, 0.53a) - Answers A
,A triangular section has coordinates of A(2, 2), B(11, 2), and C(5, 8). Find the coordinates of the centroid
of the triangular section.
a. (7, 4)
b. (6, 4)
c. (8, 4)
d. (9, 4) - Answers B
The following cross section has the following given coordinates. Compute for the centroid of the given
cross section. A(2, 2), B(5, 8), C(7, 2), D(2, 0), and E(7, 0).
a. (4.6, 3.4)
b. (4.8, 2.9)
c. (5.2, 3.8)
d. (5.3, 4.1) - Answers A
Sections ABCD is a quadrilateral having the given coordinates A(2, 3), B(8, 9), C(11, 3), and D(11, 0).
Compute for the coordinates of the centroid of the quadrilateral.
a. (5.32, 3)
b. (6.23, 4)
c. (7.33, 4)
d. (8.21, 3) - Answers C
A cross section consists of a triangle and a semi circle with AC as its diameter. If the coordinates of A(2,
6), B(11, 9), and C(14, 6). Compute for the coordinates of the centroid of the cross section.
a. (4.6, 3.4)
b. (4.8, 2.9)
c. (5.2, 3.8)
, d. (5.3, 4.1) - Answers A
A 5 m x 5 cm is cut from a corner of 20 cm x 30 cm cardboard. Find the centroid from the longest side.
a. 10.99 m
b. 11.42 m
c. 10.33 m
d. 12.42 m - Answers C
Locate the centroid of the area bounded by the parabola y2 = 4x, the line y = 4 and the y-axis.
a. (0.4, 3)
b. (0.6, 3)
c. (1.2, 3)
d. (1.33, 3) - Answers C
Find the centroid of the area bounded by the curve x2 = -(y - 4), the x-axis and the y-axis on the first
quadrant.
a. (0.25, 1.8)
b. (1.25, 1.4)
c. (1.75, 1.2)
d. (0.75, 1.6) - Answers D
Locate the centroid of the area bounded by the curve y2 = -1.5(x - 6), the x-axis and the y-axis on the
first quadrant.
a. (2.2, 1.38)
b. (2.4, 1.13)
c. (2.8, 0.63)
