Welcome to your Integration(Senior Class Math Study by Topics) NAME EMAIL PHONE NUMBER 1. Find ∫ 1/ x²+3x-10 dx In (x-2 / x-5) + C C 1/7 In (x-2 / x-5) + C 7In x + C 2. Evaluate the integrals: 14/3 12/3 12 14 3. Evaluate: -1/2 -1/3 1/3 1/2 4. An object is ejected vertically upwards from the ground at 18 m/s. Find the height of the object after 3 s. 60m 48 m 54 m 84 m 5. Evaluate: 13/3 10/3 11/3 4 6. Find∫(x + 1)(x² - 2)dx x² - 2x + C 2x - x + C x4/4 + x³/3 - x² - 2x + C x³ + 2x + C 7. Find the area bounded by the curve y = x³ -3x² -x + 3 and the x-axis 4 2.1 3.3 8 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 ∫x sin 2x dx cos2x /2 + C sin2x /2 + C -xcos2x /2 + sin2x /2+ C xcos2x /2 + sin2x /2 + C 10. Find ∫ 1 / x²-7x+10 dx In(x-5) + C 1/3 In(x-5 / x-2) + C In(x-5 / x-2) + C C 11. 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 0s, 4s 3s, 5s 1/2s, 2.4s 12. A line with equation y = 4x + 2 intersects a curve with the equation y = x² + 2 at the points M and N. Determine the coordinates of M and N M(1, 3), N(3, 12) M(2, 3), N(2, 5) M(2, 5), N(3, 18) M(0, 4), N(4, 18) 13. Evaluate: In 3 In 4 In 6 In 7 14. The gradient of a curve at P(x, y) is 3x².If the curve passes through Q(1, 5),find the equation of the curve. 3x³+4 x+4 x³+4x x³+4 15. Evaluate the definite integral: 456.43 1658.57 2456.63 324.87 16. Evaluate the definite integral: -4 4 3 5 17. The gradient of a curve is given byx² - 4x + 3If the curve passes through the point (3, 1). Find the area of the finite region enclosed by the curve, the lines x = 1, x = 3 and y = 0 6/7 5/9 8/7 10/3 18. 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 2237 sq. units 284/3 sq. units 38 sq. units 3/38 sq. units 19. The gradient of a curve is given by dy/dx = 10x - 3x². If the curve passes through the origin, find the equation of the curve. y = x³ + 5x² y = 5x² + x³ y = x³ - 5x² y = 5x² - x³ 20. Given that dv/dt = -64t and v = 10 when t = 0, find v when t = 2. v = -118 v = -64 v = 118 v = 64 21. Evaluate: 3/2 6/7 7/6 2/3 22. Find ∫1 / x(x-1) dx In (x/ x+1) + C In (x-1) + C In (x/ x-1) + C In (x+1) + C 23. Find ∫x sinx dx 1/x + C cos x + sinx + C -x cosx + sinx + C sinx + C 24. Find ∫sin 2x cos 3x dx 1/2 cosx + C -1/10 sin5x + 1/2 cosx + C -1/10 cos5x + 1/2 cosx + C 1/10 cos5x + 1/2 cosx + C 25. The gradient of a curve is given by dy/dx = 3x² - 8x + 3. If the curve passes through the origin, find the equation of the curve. y = x³ - 4x² + 3x y = x³ - 4x² - 3x y = x³ + 3x y = x³ 1 out of 25
