Integral Calculus Exam Questions and Correct Answers Latest Update 2024 (Already Passed)

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) d. (2.6, 0.88) - Answers B Locate the centroid of the area bounded by the curve 5y2 = 16x and y2 = 8x - 24 on the first quadrant. a. (2.20, 1.51) b. (1.50, 0.25) c. (2.78, 1.39) d. (1.64, 0.26) - Answers A Locate the centroid of the area bounded by the parabolas x2 = 8y and x2 = 16(y - 2) in the first quadrant. a. (3.25, 1.2) b. (2.12, 1.6) c. (2.67, 2.0) d. (2.00, 2.8) - Answers B Given the area in the first quadrant bounded by x2 = 8y, the line y - 2 = 0 and the y-axis. What is the volume generated when revolved about the line y - 2 = 0? a. 53.31 m3 b. 45.87 m3 c. 26.81 m3 d. 33.98 m3 - Answers C Given the area in the first quadrant bounded by x2 = 8y, the line x = 4 and the x-axis. What is the volume generated by revolving this area about the y-axis? a. 78.987 m3 b. 50.265 m3 c. 61.253 m3 d. 82.285 m3 - Answers B Given the area in the first quadrant bounded by x2 = 8y, the line y - 2 = 0 and the y-axis. What is the volume generated when this area is revolved about the x-axis. a. 20.32 m3 b. 34.45 m3 c. 40.21 m3 d. 45.56 m3 - Answers C Find the volume formed by revolving the hyperbola xy = 6 from x = 2 to x = 4 about the x-axis. a. 23.23 m3 b. 25.53 m3 c. 28.27 m3 d. 30.43 m3 - Answers C The region in the first quadrant under the curve y = Sinh x from x = 0 to x = 1 is revolved about the x-axis. Compute the volume of solid generated. a. 1.278 m3 b. 2.123 m3 c. 3.156 m3 d. 1.849 m3 - Answers A A square hole of side 2 cm is chiseled perpendicular to the side of a cylindrical post of radius 2 cm. If the axis of the hole is going to be along the diameter of the circular section of the post, find the volume cutoff. a. 15.3 m3 b. 23.8 m3 c. 43.7 m3 d. 16.4 m3 - Answers A Find the volume common to the cylinders x2 + y2 = 9 and y2 + z2 = 9. a. 241 m3 b. 533 m3 c. 424 m3 d. 144 m3 - Answers D Given is the area in the first quadrant bounded by x2 = 8y, the line, the line x = 4 and the x-axis. What is the volume generated by revolving this area about the y-axis. a. 50.26 m3 b. 52.26 m3 c. 53.26 m3 d. 51.26 m3 - Answers A The area bounded by the curve y2 = 12x and the line x = 3 is revolved about the line x = 3. What is the volume generated? a. 185 b. 187 c. 181 d. 183 - Answers C The area in the second quadrant of the circle x2 + y2 = 36 is revolved about the line y + 10 = 0. What is the volume generated?