Welcome to your Integration(Senior Class Math Study by Topics) NAME EMAIL PHONE NUMBER 1. Find ∫x tan²x dxIncos x+Cx(tanx- x) +In cosx + x²/2 + Cx(tanx- x) +In cosx + Cx(tanx -x) + C2. Evaluate the definite integral:5610235813. 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 m112 m138 m168 m4. Using the trapezoid rule with five ordinates at x = 1, 2, 3, 4, 5, estimate the value of10 sq. units13 sq. units11 sq. units12 sq. units5. The gradient of a curve is given byx² - 4x + 3If the curve passes through the point (3, 1). Find the equation of the curve2x² + 3x + 1y³/3 - 2x² + 3x + 1y³/3 - 2x² + 3x + 6y³/3 - 2x²6. Evaluate:283/3 sq units38/3 sq. units283 sq. units48 sq. units7. Evaluate:0.7770.6580.1630.5638. Evaluate:12/51/212/714/39. Find the area bounded by the curve y = x(2 - x), the x-axis, x=0 and x= 2.4/324310. A curve passes through the point (3, -1). If its gradient function is 2x + 5, find the equation of the curvey = x² + 5x - 25y = 3x³ + x² + 5x - 25y = 3x³ + 5x - 25y = 3x³ + x² + 5x + 2511. Evaluate the integrals:-1/5-1/21/21/512. Evaluate:correct to 3 decimal places2.8683.7972.3682.38613. 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(2, 9)(3, 1)(0, 6)(1, 7)14. 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.32 m147 m47 m132 m15. 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-2s, 9s0s, 4s3s, 5s16. 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 - 317. Find ∫x sinx dx-x cosx + sinx + Ccos x + sinx + Csinx + C1/x + C18. A curve y has gradientdy/dx = 3x² - 6x + 2.If the curve passes through the origin, find its equation.y = x(x-1)(x-2)y = 1-xy = x(x+5)y = x + 219. Evaluate the definite integral:3-44520. Find the area of the region lying below the x-axis and bounded by the parabola y = x(x - 2) and the x-axis.4/33/43/22/321. Evaluate the integrals:12611322. 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, 5), N(3, 18)M(2, 3), N(2, 5)M(1, 3), N(3, 12)M(0, 4), N(4, 18)23. 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(4, 0)(1, 2)(11/3, 9)(1, 7/3)24. Find the area bounded by the given pairs of curves y = x² - x + 3 and y = 31/51/31/61/225. 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 = 3682426 out of 25