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 the integrals:10620132. 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 instant21.54 m54.75 m12.47 m43.45 m3. Calculate the area under the line y = x + 2 between the limits x = 0 and x = 10556070504. Evaluate the definite integral:1023581565. Evaluate:13/3411/310/36. 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.132 m47 m32 m147 m7. 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/s0.5 m/s12 m/s24 m/s8. Calculate the area of the finite region bounded by the curve y = 4x - x² and the x-axis23/443/834/1132/39. The gradient of a curve which passes through the point ( 1, 2) is given by x². Determine the equation of the curve.y = 3x³ + 3/5y = 1/3 x³ + 5/3y = x³ + 2xy = 1/3 x³ - 5/310. 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 - 5y = x² - 6xy = x - 18y = x² - 6x - 311. 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 + 8y = x² + 6y = x² + 6x + 8y = x - 312. Evaluate ∫1/x(x + 2) dx, x ≠ 0, -21/2 In(x / x+2) + Cx + 2 + C2In(x+2 / x) + Cx/2 + C13. Find the area bounded by the curve y =x(x - 1) and the line y = 3x32/335112314. 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 = 3864215. The gradient of a curve is given byx² - 4x + 3If the curve passes through the point (3, 1). Find the area of the finite region enclosed by the curve, the lines x = 1, x = 3 and y = 05/96/710/38/716. Find ∫x sin 2x dxsin2x /2 + C-xcos2x /2 + sin2x /2+ Cxcos2x /2 + sin2x /2 + Ccos2x /2 + C17. 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(1, 3), N(3, 12)M(2, 5), N(3, 18)M(2, 3), N(2, 5)M(0, 4), N(4, 18)18. 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, 2.4s3s, 5s0s, 4s-2s, 9s19. The velocity of a particle, v m/s, after t s is given by v = t² + 5. Find the distance travelled at the end of 3 s.24 m18 m48 m3 m20. Evaluate the integrals:14/312/3121421. Evaluate:6- 2In58In 510/3 - 5In34/5In 322. A curve passes through the point (3, -1). If its gradient function is 2x + 5, find the equation of the curvey = 3x³ + 5x - 25y = 3x³ + x² + 5x + 25y = 3x³ + x² + 5x - 25y = x² + 5x - 2523. Find ∫x tan²x dxIncos x+Cx(tanx- x) +In cosx + Cx(tanx- x) +In cosx + x²/2 + Cx(tanx -x) + C24. Find the area of the region lying below the x-axis and bounded by the parabola y = x(x - 2) and the x-axis.3/42/34/33/225. 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 equation3x²+11x-602x³+11x-6011x-602x³-3x²+11x-6026 out of 25
