02/04/2020Integration(Senior Class Math Study by Topics) 0Comments by Gate Academy Welcome to your Integration(Senior Class Math Study by Topics) NAME EMAIL PHONE NUMBER 1. Evaluate ∫1/x(x + 2) dx, x ≠ 0, -2 x/2 + C 2In(x+2 / x) + C 1/2 In(x / x+2) + C x + 2 + C2. Given that dy/dx = 6x² + 5x, find the function which passes through the point (2, 30). y = 2x³ + 5/2 x² + 4 y = x³ + 2x² + 4 y = 6x² + 5x y = 2x³ + 5/2 x² - 43. Evaluate the definite integral: 324.87 456.43 2456.63 1658.574. Evaluate the integrals: 1/2 -1/2 1/5 -1/55. 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 = x - 3 y = x² + 6 y = x² + 6x + 86. 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 = 5x² - x³ + 4 y = 5x² - x³ y = 5x³ - x² + 87. Find ∫sin 2x cos 3x dx -1/10 sin5x + 1/2 cosx + C -1/10 cos5x + 1/2 cosx + C 1/2 cosx + C 1/10 cos5x + 1/2 cosx + C8. Find ∫ sin x cos 3x dx -1/8 cos4x + 1/4 cos2x + C -1/8 cos4x + 1/4 sin2x + C 1/4 cos2x + C 1/8 cos4x + 1/4 sin2x + C9. Find ∫1 / x(x-1) dx In (x/ x+1) + C In (x+1) + C In (x-1) + C In (x/ x-1) + C10. 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 21/4 32/3 11/2 1211. Evaluate: 0.777 0.658 0.163 0.56312. Evaluate:correct to 3 decimal places 2.868 2.386 2.368 3.79713. Find the area of the finite region bounded by the curve y = 5 - 4x - x² and the linesy = 0, x= 0 and x = -5 3/100 9/2 100/3 2/914. The gradient of a curve which passes through the point (1, 2) is 3+2x. Find its equation. y = x²+ 3x - 2 y = x³ + 2x² - 2 y = x³ + 2x²+ 3x y = x³ + 2x²+ 3x - 215. 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? 168 m 144 m 138 m 112 m16. 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 9/8 6/7 7/8 5/617. 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 9/3 4 1118. Evaluate the integrals: 10 13 20 619. Evaluate: 157/6 6/157 3/19 19/320. 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 = 3t³ - 2t² - 31 x = t³ - 2t - 31 x = t³ - 2t² - 3121. Using the trapezoid rule with five ordinates at x = 1, 2, 3, 4, 5, estimate the value of 13 sq. units 12 sq. units 10 sq. units 11 sq. units22. 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 1/4 1/3 1/223. Find the area of the curve y = 2x² + 5, x-axis from 0 and 3 53 14 22 3324. 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 distance from 0 at this instant 54.75 m 21.54 m 12.47 m 43.45 m25. Find ∫ 1 / x²-7x+10 dx C In(x-5) + C In(x-5 / x-2) + C 1/3 In(x-5 / x-2) + C26 out of 25
