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: 48 sq. units 283/3 sq units 283 sq. units 38/3 sq. units 2. Evaluate: 157/6 6/157 19/3 3/19 3. 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. 1/2s, 2.4s 0s, 4s 3s, 5s -2s, 9s 4. 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) (11/3, 9) (4, 0) (1, 7/3) 5. Evaluate ∫ x / x+3 dx In(x + 3) + C C x-3 + C x - 3 In(x+3) + C 6. The velocity of a particle is given by v =3t² + 8t. Find the distance travelled by the particle between t = 3 s and t = 5 s. 158 m 224 m 162 m 144 m 7. Using the trapezoid rule with five ordinates at x = 1, 2, 3, 4, 5, estimate the value of 10 sq. units 12 sq. units 11 sq. units 13 sq. units 8. A curve y has gradientdy/dx = 3x² - 6x + 2.If the curve passes through the origin, find its equation. y = x(x+5) y = x + 2 y = x(x-1)(x-2) y = 1-x 9. 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 = 5x³ - x² + 8 y = x² -4 y = 5x² - x³ + 4 10. The table below shows the velocity V m/s of a particle in a relation to time t s within a period of t secondst 0 1 2 3 4 5 6V 10 12 15 16 11 5 3Use trapezoid rule:1/2 h(y1 +2y2 + 2y3 + ... + yn)Find the approximate distance traveled 65.5 sq. units 60.5 sq. units 63.5 sq units 6.5 sq. units 11. 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 + 3x + 1 y³/3 - 2x² 2x² + 3x + 1 y³/3 - 2x² + 3x + 6 12. Find ∫ 1 / x²-7x+10 dx 1/3 In(x-5 / x-2) + C In(x-5 / x-2) + C C In(x-5) + C 13. 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 3/38 sq. units 38 sq. units 14. Find the area of the finite regions included between the curve in a curve y with gradient dy/dx = 3x² - 6x + 2 and the x-axis 2 1/2 1/3 1/4 15. A curve passes through the point (3, -1). If its gradient function is 2x + 5, find the equation of the curve y = 3x³ + x² + 5x + 25 y = 3x³ + 5x - 25 y = x² + 5x - 25 y = 3x³ + x² + 5x - 25 16. Evaluate: 12/5 12/7 14/3 1/2 17. Evaluate the integrals: 12 11 6 3 18. An object travels in a straight line with velocity, v m/s at time t s is given by v = 3t² + 7. What is the distance travelled by the object from t = 2 s to t = 5 s? 144 m 138 m 168 m 112 m 19. 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 6/7 5/6 7/8 9/8 20. Find ∫ 1/ x(x+1) dx In(x+1) +C In(x / x-1) + C In(x-1) + C In(x / x+1) + C 21. Evaluate the integrals: 13 10 6 20 22. 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 y = x³ - 4x² + 3x y = x³ + 3x y = x³ - 4x² - 3x 23. 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 4 8 2 6 24. The gradient of a curve which passes through the point ( 1, 2) is given by x². Determine the equation of the curve. y = 1/3 x³ - 5/3 y = x³ + 2x y = 1/3 x³ + 5/3 y = 3x³ + 3/5 25. Find ∫ x / 2x+3 dx 1/2 x -3/4 In(2x+3) + C In(2x+3) + C 1/2 x -3/4 In(2x+3) 1/2 x +C 1 out of 25
