02/04/2020 Integration(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. The gradient of a curve is given byx² - 4x + 3If the curve passes through the point (3, 1). Find the equation of the curvey³/3 - 2x² + 3x + 12x² + 3x + 1y³/3 - 2x² + 3x + 6y³/3 - 2x²2. Evaluate:283/3 sq units48 sq. units283 sq. units38/3 sq. units3. An object is ejected vertically upwards from the ground at 18 m/s. Find the height of the object after 3 s.60m54 m48 m84 m4. Find ∫ 1/ x²+3x-10 dx1/7 In (x-2 / x-5) + C7In x + CCIn (x-2 / x-5) + C5. Using the trapezoid rule with five ordinates at x = 1, 2, 3, 4, 5, estimate the value of13 sq. units11 sq. units12 sq. units10 sq. units6. Find ∫ x / 2x+3 dx1/2 x +C1/2 x -3/4 In(2x+3)In(2x+3) + C1/2 x -3/4 In(2x+3) + C7. Evaluate:3/22/36/77/68. Find the area bounded by the curve y = x(2 - x), the x-axis, x=0 and x= 2.4/34239. Evaluate:10/313/3411/310. 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.0s, 4s1/2s, 2.4s-2s, 9s3s, 5s11. Evaluate the definite integral:456.432456.631658.57324.8712. With the curve y = (x-3)². Find the area of the finite region enclosed between the curve and the x and y axes11949/313. 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.2732π3227π14. 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 = t³ - 2t - 31x = 3t³ + 2t² - 31x = 3t³ - 2t² - 31x = t³ - 2t² - 3115. 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 instant43.45 m21.54 m12.47 m54.75 m16. Evaluate:∫ 1 / x²(1-4x)4In(x / 1-4x) - 1/x + CC4(x / 1-4x) + CInx + C17. 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.144 m162 m224 m158 m18. Evaluate:3/1919/3157/66/15719. Evaluate the integrals:31261120. Evaluate:1/212/512/714/321. Find ∫x cos2x dxC1/2 x sin 2x + 1/4 cos 2x + Ccos4x + C1/2 x sin2x + C22. A curve passes through the point (3, -1). If its gradient function is 2x + 5, find the equation of the curvey = 3x³ + x² + 5x + 25y = 3x³ + 5x - 25y = 3x³ + x² + 5x - 25y = x² + 5x - 2523. Find the area bounded by the curve y = x³ -3x² -x + 3 and the x-axis3.382.1424. 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 NM(2, 3), N(2, 5)M(2, 5), N(3, 18)M(0, 4), N(4, 18)M(1, 3), N(3, 12)25. Find ∫x² log x dxx/4 + logx + CCx³/3 logx - x³/6 + Cxlogx + C26 out of 25
