02/04/2020 Integration(Senior Class Math Study by Topics) 02/04/2020 0Comments by Gate Academy Welcome to your Integration(Senior Class Math Study by Topics) NAME EMAIL PHONE NUMBER 1. The finite are enclosed by the curve y² = 4x and the line x = 4 is rotated through 360° about the x-axis. Find the volume of the solid generated in cubic units. 32 27 27π 32π 2. Evaluate: 283 sq. units 38/3 sq. units 283/3 sq units 48 sq. units 3. Given that dy/dx = 6x² + 5x, find the function which passes through the point (2, 30). y = 2x³ + 5/2 x² - 4 y = x³ + 2x² + 4 y = 6x² + 5x y = 2x³ + 5/2 x² + 4 4. Find∫(x + 1)(x² - 2)dx x² - 2x + C x³ + 2x + C x4/4 + x³/3 - x² - 2x + C 2x - x + C 5. Evaluate the definite integral: -10/3 12/5 -3 -4 6. The gradient of a curve is given by dy/dx = 10x - 3x². If the curve passes through the point (-1, 10), find the equation of the curve y = 5x³ - x² + 8 y = 5x² - x³ y = x² -4 y = 5x² - x³ + 4 7. Find ∫ x / 2x+3 dx 1/2 x -3/4 In(2x+3) + C 1/2 x +C 1/2 x -3/4 In(2x+3) In(2x+3) + C 8. The gradient of a curve that passes through the point (-2, 6) is given by x. Determine the equation of the curve. y = x² - 4 y = 1/2 x² + 4 y = x² + 4 y = -1/2 x² - 4 9. Find ∫x² log x dx C xlogx + C x³/3 logx - x³/6 + C x/4 + logx + C 10. Find, in square units, the area of the finite region bounded by the curve y = x² + 4x + 2, andlines y = 0, x = 4 and x = 6 284/3 sq. units 2237 sq. units 38 sq. units 3/38 sq. units 11. Evaluate the integrals: 20 10 6 13 12. Find ∫ sin x cos 3x dx 1/4 cos2x + C -1/8 cos4x + 1/4 cos2x + C 1/8 cos4x + 1/4 sin2x + C -1/8 cos4x + 1/4 sin2x + C 13. Find in square units, the area of the finite region bounded by the curve y = x³ - x and the x-axis, from x = -1 to x =1 1/2 2 1/3 1/4 14. The velocity v m/s of a body moving at any time t, is given by v = 2t² - 1/3t³ + 10, determine the values of t at which the acceleration of the particle is zero. -2s, 9s 1/2s, 2.4s 3s, 5s 0s, 4s 15. The acceleration of a particle moving in a straight line is given by a = 3t² - 4t. Find the expressions for the velocity given that v = 0 m/s and t = 0 s. v = t³ - 2t v = 2t³ - t² v = t³ - 2t² v = t³ + 2t² 16. The gradient of a curve which passes through the point (1, -5) is given by 4x. Determine the equation of the curve. y = -2x² - 7 y = x² - 14 y = -2x² + 7 y = 2x² - 7 17. Evaluate the definite integral: 27 33/4 45/2 32/5 18. Evaluate the integrals: 3 11 12 6 19. Find ∫ 1/ x²+3x-10 dx 1/7 In (x-2 / x-5) + C 7In x + C C In (x-2 / x-5) + C 20. Given that x and t are two variables such that dx/dt = 3t² - 4t, and x = 1 when t = 4, express x in terms of t. x = t³ - 2t - 31 x = 3t³ + 2t² - 31 x = 3t³ - 2t² - 31 x = t³ - 2t² - 31 21. Evaluate: 10/3 4 13/3 11/3 22. Evaluate:correct to 3 decimal places 2.368 3.797 2.386 2.868 23. Evaluate the integrals: 12 14/3 14 12/3 24. A body is projected from a point O in a straight line with an initial velocity of 10 m/s. If the acceleration is 5t² + 3t, find the distance from 0 at this instant 21.54 m 12.47 m 43.45 m 54.75 m 25. Evaluate: In 3 In 7 In 6 In 4 1 out of 25
