Welcome to your Integration(Senior Class Math Study by Topics) NAME EMAIL PHONE NUMBER 1. The gradient of a curve which passes through the point ( 1, 2) is given by x². Determine the equation of the curve. y = x³ + 2x y = 1/3 x³ - 5/3 y = 3x³ + 3/5 y = 1/3 x³ + 5/3 2. Evaluate:correct to 3 decimal places 2.386 2.368 2.868 3.797 3. Using the trapezoid rule with five ordinates at x = 1, 2, 3, 4, 5, estimate the value of 12 sq. units 11 sq. units 10 sq. units 13 sq. units 4. The velocity of a particle, v m/s, after t s is given by v = t² + 5. Find the distance travelled at the end of 3 s. 18 m 48 m 24 m 3 m 5. Find ∫ (2+x)/x dx, x > 0. In 2x + x + C In x² + x + C In 2x + C ln x³ +x + C 6. Find the area bounded by the given pairs of curves y = x² - x + 3 and y = 3 1/2 1/3 1/6 1/5 7. Find ∫cos2x cos 3x dx 1/10 sin 5x + C -1/10 sin 5x + 1/2 sinx + C 1/10 sin 5x + 1/2 cosx + C 1/10 sin 5x + 1/2 sinx + C 8. Find the area bounded by the curve y = x³ -3x² -x + 3 and the x-axis 8 4 3.3 2.1 9. Find ∫ x / 2x+3 dx 1/2 x -3/4 In(2x+3) + C 1/2 x -3/4 In(2x+3) 1/2 x +C In(2x+3) + C 10. 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 11. Find ∫x tan²x dx x(tanx- x) +In cosx + x²/2 + C Incos x+C x(tanx -x) + C x(tanx- x) +In cosx + C 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 the integrals: 6 20 13 10 14. ∫(sinx- 5cosx)dx sinx + C -cosx -5sinx + C cosx + 5sinx + C cosx - 2sinx + C 15. Evaluate:∫ 1 / x²(1-4x) 4(x / 1-4x) + C C Inx + C 4In(x / 1-4x) - 1/x + C 16. 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 1/3 1/4 1/2 2 17. Evaluate the definite integral: 102 81 35 56 18. Evaluate: 4 11/3 13/3 10/3 19. The gradient of a curve at any point (x, y) is given by dy/dx = 2(x - 3) and the point(3, -12) lies on the curve. Find the equation of the curve. y = x² - 6x - 5 y = x² - 6x - 3 y = x - 18 y = x² - 6x 20. Find the area bounded by the curve y = -5 + 6x - x² and the x-axis 43 32/3 12 24.7 21. 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 = x² -4 y = 5x³ - x² + 8 y = 5x² - x³ y = 5x² - x³ + 4 22. 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 8/7 10/3 5/9 23. The gradient of a curve is given byx² - 4x + 3If the curve passes through the point (3, 1). Find the equation of the curve y³/3 - 2x² y³/3 - 2x² + 3x + 1 2x² + 3x + 1 y³/3 - 2x² + 3x + 6 24. An object is ejected vertically upwards from the ground at 18 m/s. Find the height of the object after 3 s. 48 m 54 m 60m 84 m 25. 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 velocity after 3 seconds. 58.5 m/s 60 m/s 68.5 m/s 48 m/s 1 out of 25