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. Evaluate: 1/2 -1/2 -1/3 1/3 2. The gradient of a curve is given byx² - 4x + 3If the curve passes through the point (3, 1). Find the maximum point on the curve (1, 2) (4, 0) (11/3, 9) (1, 7/3) 3. 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(0, 4), N(4, 18) M(1, 3), N(3, 12) M(2, 5), N(3, 18) M(2, 3), N(2, 5) 4. Find the area bounded by the curve y = x³ -3x² -x + 3 and the x-axis 3.3 2.1 4 8 5. Calculate the area of the finite region bounded by the curve y = x² + 4x - 12, the x-axis and the ordinates x = 1 and x = 3 2 8 4 6 6. The gradient of a curve is given byx² - 4x + 3If the curve passes through the point (3, 1). Find the minimum point on the curve (2, 9) (1, 7) (0, 6) (3, 1) 7. Using the trapezoid rule with five ordinates at x = 1, 2, 3, 4, 5, estimate the value of 12 sq. units 13 sq. units 11 sq. units 10 sq. units 8. 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 = 5x² - x³ y = x³ + 5x² y = x³ - 5x² y = 5x² + x³ 9. 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 = 3t³ - 2t² - 31 x = t³ - 2t² - 31 x = 3t³ + 2t² - 31 x = t³ - 2t - 31 10. Evaluate the definite integral: -10/3 -3 12/5 -4 11. Find ∫sin2x sin3x dx -1/10 sin5x + 1/2 cosx + C 1/10 sin5x + 1/2 sinx + C -1/10 sin5x + 1/2 sinx + C 1/2 cosx + C 12. 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 - 2t² v = t³ - 2t v = 2t³ - t² v = t³ + 2t² 13. Evaluate: In 4 In 7 In 3 In 6 14. Given that dy/dx = 6x² + 5x, find the function which passes through the point (2, 30). y = 2x³ + 5/2 x² + 4 y = 2x³ + 5/2 x² - 4 y = 6x² + 5x y = x³ + 2x² + 4 15. The gradient of a curve at any point (x,y) is 6x² - 6x + 11. If the curve passes through the point (3, 0), find its equation 2x³+11x-60 11x-60 3x²+11x-60 2x³-3x²+11x-60 16. Evaluate: 12/5 12/7 14/3 1/2 17. Evaluate:∫ 1 / x²(1-4x) 4In(x / 1-4x) - 1/x + C 4(x / 1-4x) + C Inx + C C 18. Evaluate: 3/2 2/3 7/6 6/7 19. The gradient of the curve that passes through the point (1, -10) is given by 3x² - 6. Find the equation of the curve. y = x³ + 5 y = x³ - 30 y = x³ + 6x - 5 y = x³ - 6x - 5 20. Evaluate the definite integral: -1 1 0 5 21. With the curve y = (x-3)². Find the area of the finite region enclosed between the curve and the x and y axes 9 11 4 9/3 22. Find ∫ 1/ x(x+1) dx In(x / x+1) + C In(x / x-1) + C In(x-1) + C In(x+1) +C 23. Evaluate the definite integral: 33/4 45/2 32/5 27 24. Calculate the area of the finite region bounded by the curve y = 4x - x² and the x-axis 32/3 43/8 34/11 23/4 25. 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 38 sq. units 284/3 sq. units 3/38 sq. units 2237 sq. units 1 out of 25