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: 6- 2In5 8In 5 4/5In 3 10/3 - 5In3 2. Evaluate: 1/3 -1/2 -1/3 1/2 3. The gradient of a curve which passes through the point (1, 2) is 3+2x. Find its equation. y = x³ + 2x²+ 3x - 2 y = x³ + 2x² - 2 y = x²+ 3x - 2 y = x³ + 2x²+ 3x 4. Find the area bounded by the curve y =x(x - 1) and the line y = 3x 32/3 11 23 35 5. 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 6. The line 2y = x + 2 intersects the curve y = 1/4 (7x-x²). Calculate the area of the finite region bounded by the curve and the line 7/8 6/7 5/6 9/8 7. 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 8. A body starting from the origin O moves in a straight line, and its velocity, v m/s, after t s is given by v = 12 + 20t - 3t². Calculate the distance moved by the particle in 2 s. 32 m 44 m 56 m 78 m 9. Find the area of the region lying below the x-axis and bounded by the parabola y = x(x - 2) and the x-axis. 3/2 2/3 3/4 4/3 10. 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 = 5x² - x³ y = x² -4 y = 5x³ - x² + 8 y = 5x² - x³ + 4 11. 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 11x-60 2x³-3x²+11x-60 2x³+11x-60 3x²+11x-60 12. 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 - 30 y = x³ + 6x - 5 y = x³ + 5 y = x³ - 6x - 5 13. Given that y and x are two variables such that dy/dx = 2x - 6, and y = -1 when x = 3, express y in terms of x. y = x² - 6x + 8 y = x² + 6x + 8 y = x² + 6 y = x - 3 14. A line with equation y = 4x + 2 intersects a curve with the equation y = x² + 2 at the points M and N. Evaluate the area enclosed between the curve and the line 32/3 12 21/4 11/2 15. 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 3/38 sq. units 2237 sq. units 38 sq. units 16. 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. 3s, 5s -2s, 9s 1/2s, 2.4s 0s, 4s 17. 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(2, 3), N(2, 5) M(1, 3), N(3, 12) M(0, 4), N(4, 18) M(2, 5), N(3, 18) 18. Evaluate the integrals: 6 11 12 3 19. Find ∫ x Inx dx xe +C xIn x + C Inx + C x² Inx - x²/4 + C 20. Find ∫ x / 2x+3 dx 1/2 x +C In(2x+3) + C 1/2 x -3/4 In(2x+3) 1/2 x -3/4 In(2x+3) + C 21. 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. 32π 27π 27 32 22. 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 2 1/2 23. The acceleration of a moving particle at the end of t seconds is given by (5 - t) m/s². If the particle starts from rest, find its velocity at the end of 4 s? 4 m/s 12 m/s 24 m/s 0.5 m/s 24. 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 (4, 0) (1, 7/3) (1, 2) (11/3, 9) 25. Find ∫ 1/ x²+3x-10 dx 1/7 In (x-2 / x-5) + C C 7In x + C In (x-2 / x-5) + C 1 out of 25
