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:14/31/212/512/72. Calculate the area of the finite region bounded by the curve y = 4x - x² and the x-axis32/334/1143/823/43. Find the area of the finite region bounded by the curve y = 5 - 4x - x² and the linesy = 0, x= 0 and x = -5100/39/23/1002/94. Evaluate the integrals:14/3141212/35. 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 + 5y = x³ - 6x - 5y = x³ + 6x - 5y = x³ - 306. 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 =11/421/21/37. Find ∫x² log x dxCx³/3 logx - x³/6 + Cx/4 + logx + Cxlogx + C8. Evaluate the definite integral:015-19. Find ∫ sin x cos 3x dx-1/8 cos4x + 1/4 cos2x + C-1/8 cos4x + 1/4 sin2x + C1/4 cos2x + C1/8 cos4x + 1/4 sin2x + C10. 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.18 m24 m3 m48 m11. Find ∫ (2+x)/x dx, x > 0.ln x³ +x + CIn 2x + CIn x² + x + CIn 2x + x + C12. The gradient of a curve that passes through the point (-2, 6) is given by x. Determine the equation of the curve.y = x² - 4y = x² + 4y = -1/2 x² - 4y = 1/2 x² + 413. The acceleration of a particle moving in a straight line is given by a = 3t² - 4t. Find the expressions for the velocity given that v = 0 m/s and t = 0 s.v = 2t³ - t²v = t³ - 2tv = t³ + 2t²v = t³ - 2t²14. Find ∫ 1/ x(x+1) dxIn(x-1) + CIn(x / x+1) + CIn(x+1) +CIn(x / x-1) + C15. Find the area of the curve y = 2x² + 5, x-axis from 0 and 31422335316. Evaluate:11/313/310/3417. Find the area bounded by the curve y = x(2 - x), the x-axis, x=0 and x= 2.34/32418. Find the area bounded by the given pairs of curves y = x² - x + 3 and y = 31/31/21/51/619. 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+4x³+4xx+4x³+420. 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(0, 4), N(4, 18)M(1, 3), N(3, 12)21. Evaluate the integrals:10-1222. With the curve y = (x-3)². Find the area of the finite region enclosed between the curve and the x and y axes9119/3423. The velocity of a particle is given by v =3t² + 8t. Find the acceleration when t = 8s8 m/s²18 m/s²23 m/s²56 m/s²24. Find ∫ x / 2x+3 dx1/2 x -3/4 In(2x+3)In(2x+3) + C1/2 x -3/4 In(2x+3) + C1/2 x +C25. Find the area bounded by the curve y = x³ -3x² -x + 3 and the x-axis2.1843.326 out of 25
