Integral Edge

MASTERY QUESTION GUIDES IN INTEGRAL CALCULUS 1. Find the ∫(x+1)/√x dx a. 2/3 x√x + 2√x + C b. 2/3 x√x - 2√x + C c. 1/3 x√x + 2√x + C d. 1/3 x√x - 2√x + C 2. Evaluate ∫x sinx dx a. sinx-xcosx + C b. sinx+xcosx + C c. cosx-xsinx + C d. cosx+xcosx + C 3. What is the integral of x(x+1)⁸dx if the lower limit is 0 and upper limit is 1? a. 22.76 b. 34.76 c. 46.76 d. 45.52 4. Evaluate the improper integral ∫dx/(1+x²) from -ꝏ to +ꝏ. a. pi b. 2pi c. pi/2 d. pi/4 5. Evaluate the iterated integral: ∫∫x³dydx from 0 to 1 (outer integral) and from 0 to 4 (inner integral). a. 1 b. 2 c. 3 d. 4 6. Find the value of ∫∫x^3ydydx if 0 ≤ x ≤ 2y and 1 ≤ y ≤ 2. a. 24 b. y² c. 42 d. x² 7. What is the integral of 12sin⁵xcos⁵xdx if the lower limit is zero and upper limit is pi/2? a. 0.1 b. 0.2 c. 0.3 d. 0.4 8. Find the area bounded by the parabola y=x² and x=y². a. 1/3 b. ½ c. 2/3 d. 1 9. What is the area bounded by the curve y=x³, the x-axis and the lines x=-2 and x=1? a. 2.45 b. 4.25 c. 5. 24 d. 5.42 10. Find the area bounded by the curve y=sinx and the x-axis between x=0 and x=4pi. a. 2 b. 4 c. 6 d. 8 11. Find the area bounded by y=e^x, x=0 and y=0. a. 1 b. 2 c. e d. ꝏ 12. Find the area of the region between the curve y=x³ and the lines y=-x and y=1. a. 5/4

b. ¾ c. ¼ d. 2/3 13. Determine the region under the curve √x + √y =1 and the first quadrant. a. 1/2 b. 1/3 c. 1/8 d. 1/6 14.Find the length of the curve formed by the parabola y=x² + 2x from x=0 to x=1. a. 1.15 b. 3.17 c. 2.45 d. 4.92 15. Find the length of arc in one branch of the curve y² = x³ from x=0 to x=1. a. 1.2 b. 1.44 c. 1.64 d. 1.84 16. This refers to the inverse process of determining a function whose derivative is known is called: a. integration b. evolution c. antidifferentiation d. involution 17. An integration resulting to an antiderivative of a certain with an arbitrary constant. a. definite integration b. integration by parts c. indefinite integration d. integration by substitution 18. The function y=f(x) is an even function if: a. f(-x)=f(x) b. f(-x)=-f(x) c. f(-x)=f’(x) d. f(-x)=-f’(x) 19. The function y=f(x) is an odd function if: a. f(-x)=f(x) b. f(-x)=-f(x) c. f(-x)=f’(x) d. f(-x)=-f’(x) 20. The function to be integrated a. definite integral b. indefinite integral c. integrand d. integers 21. Functions which are not algebraic a. transcendental functions b. explicit functions c. implicit functions d. identity functions 22. A closed curved surface having a hole in it like a tire inner tube. a. cardioid b. torus c. hypocycloid d. helix 23. The surface area of a solid of revolution is equal to the length of the generating arc times the circumference of the circle described by the centroid of the arc, provided that the axis of revolution does not cross the generating arc. a. First proposition of Pappus Theorem b. Second proposition of Pappus Theorem c. Third proposition of Pappus Theorem

d. Fourth proposition of Pappus Theorem 24. The volume of a solid of revolution is equal to the generating area times the circumference of the circle described by the centroid of the arc, provided that the axis of revolution does not cross the generating arc. a. First proposition of Pappus Theorem b. Second proposition of Pappus Theorem c. Third proposition of Pappus Theorem d. Fourth proposition of Pappus Theorem 25. A series of number where the succeeding term is greater than the preceding term. a. convergent series b. divergent series c. Fourier series d. power series 26. Find the centroid of the area under the curve y=4-x² in the first quadrant. a. (0.6, 1.6) b. (0.75, 1.8) c. (0.6, 1.8) d. (0.75, 1.6) 27. Determine the distance of the centroid from the x-axis for the area bounded by the curves y²=4x, x=0 and y=4. a. 3.2 b. 3.0 c. 1.0 d. 1.2 28. Determine the volume generated by revolving the region bounded by the curve y=x³ and the line y=1 from x=0 to x=1 about the x-axis. a. 6pi/7 b. 7pi/8 c. 5pi/6 d. 2pi/3 29. Determine the volume generated by revolving the region bounded by the curve y=1 + x² and y=5 about the x-axis. a. 282 b. 228 c. 281 d. 218 30. Find the volume generated by the region bounded by the curve y²=12x and the line x=3, rotated about the line x=3. a. 161 b. 171 c. 181 d. 191 31. Find the volume generated when the area bounded by the curve y²=x, the line x=4 and the x-axis is revolved about the y-axis. a. 75.3 b. 93.5 c. 80.4 d. 45.3 32. Find the volume generated by revolving the hyperbola xy=6 about the x-axis from x=2 to x=4. a. 4pi b. 9pi c. 12pi d. 16pi 33. Determine the surface area generated if the line segment intercepted by the coordinate axis is revolved about the y-axis. Assume the equation of the line 3x+4y-12=0. a. 20pi b. 15pi c. 10pi d. 25pi

34. Find the volume formed by revolving the ellipse 4x²+9y²=36 about the line x=5. a. 30pi b. 60pi c. 30pi² d. 60pi² 35. A 5-lb monkey is attached to the end of a 30-ft hanging rope that weighs 0.2 lb/ft. The monkey climbs the rope to the top. How much work has it done? a. 500ft-lb b. 240ft-lb c. 800ft-lb d. 120ft-lb 36. A conical tank that is 5 meters high has a radius of 2 meters, and is filled with a liquid that weighs 800 kg per cubic meter. How much work is done in discharging all the liquid at a point 3 meters above the top of the tank? a. 21,256pi kg-m b. 21,896pi kg-m c. 23,547pi kg-m d. 22,667 pi kg-m 37. Calculate the work done in pumping out the water filing a hemispherical reservoir 3m deep. a. 550 kJ b. 450 kJ c. 325 kJ d. 624 kJ 38. Find the moment of inertia of the area bounded by the curve x²=4y, the line y=1 and the y-axis on the first quadrant with respect to the x-axis. a. 8/15 b. 4/7 c. 16/15 d. 8/7 39. Find the moment of inertia of the area bounded by the curve x²=4y, the line y=1 and the y- axis on the first quadrant with respect to the y-axis. a. 8/15 b. 4/7 c. 16/15 d. 8/7 40. What is the average (mean) value of 3t³-t² over the interval -1 ≤ t ≤ 2? a. 11/4 b. 7/2 c. 8 d. 33/4