Welcome to your Integration(Senior Class Math Study by Topics) NAME EMAIL PHONE NUMBER 1. Find the area bounded by the curve y =x(x - 1) and the line y = 3x 35 23 11 32/3 2. 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 - 6x - 5 y = x³ - 30 y = x³ + 5 y = x³ + 6x - 5 3. Find ∫1 / x(x-1) dx In (x/ x+1) + C In (x+1) + C In (x/ x-1) + C In (x-1) + C 4. 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 5. 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 2 1/2 1/3 1/4 6. ∫(sinx- 5cosx)dx cosx + 5sinx + C -cosx -5sinx + C cosx - 2sinx + C sinx + C 7. 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 27 32 27π 8. A particle moves in a straight line with a velocity v in m/s at time t is given by v = 3t² +10. Calculate the distance it travels from t = 2s to t = 5s. 47 m 147 m 132 m 32 m 9. Find the area bounded by the curve y = x(2 - x), the x-axis, x=0 and x= 2. 4 4/3 3 2 10. Find ∫sin 2x cos 3x dx -1/10 cos5x + 1/2 cosx + C 1/2 cosx + C 1/10 cos5x + 1/2 cosx + C -1/10 sin5x + 1/2 cosx + C 11. ∫sin 5x dx -1/5 cos5x + C 1/5cos5x + C -1/5 sin 5x + C 1/5sinx + C 12. 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 (3, 1) (2, 9) (0, 6) (1, 7) 13. Evaluate the definite integral: 1658.57 456.43 2456.63 324.87 14. Evaluate the definite integral: -4 -3 12/5 -10/3 15. 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 16. 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 - 3 y = x - 18 y = x² - 6x - 5 y = x² - 6x 17. Evaluate: 10/3 13/3 4 11/3 18. Find ∫ (2+x)/x dx, x > 0. In 2x + C ln x³ +x + C In x² + x + C In 2x + x + C 19. Find the area of the region lying below the x-axis and bounded by the parabola y = x(x - 2) and the x-axis. 3/4 3/2 4/3 2/3 20. The gradient of a curve is given byx² - 4x + 3If the curve passes through the point (3, 1). Find the equation of the curve 2x² + 3x + 1 y³/3 - 2x² + 3x + 6 y³/3 - 2x² + 3x + 1 y³/3 - 2x² 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 4 9/3 9 11 22. Evaluate the integrals: 13 6 20 10 23. Find ∫ 1 / x²-7x+10 dx C 1/3 In(x-5 / x-2) + C In(x-5 / x-2) + C In(x-5) + C 24. Find ∫x cos2x dx 1/2 x sin2x + C 1/2 x sin 2x + 1/4 cos 2x + C cos4x + C C 25. Find ∫ sin x cos 3x dx -1/8 cos4x + 1/4 sin2x + C 1/4 cos2x + C 1/8 cos4x + 1/4 sin2x + C -1/8 cos4x + 1/4 cos2x + C 1 out of 25