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- Use graphical differentiation to verify that ddxex=ex.Use the substitution u = 4x + 2x to evaluate the indefinite integral below. (8x + 2)/ 4x2 + 2x dx Write the integrand in terms of u. (8x+2)4x+ 2x dx = du Evaluate the integral. [(8x + 2)4x + 2x dx= 0 Enter your answer in each of the answer boxes.Evaluate the definite integral 6. (2x + 3)dx 3.
- One of the correct steps to evaluate x²lnx dx to yield the correct integral (A x2 – 2 | dx x³Inx В x² dx 3 3 x²Inx x³ dx 2 2 D None E dxFind the indefinite integral and check the result by differentiation. [(5x² + √(31x132) dx Step 1 To obtain the given integral, rewrite the integral as √ [5x² + 3x1²2] dx = √ [5x² + Submit Skip (you cannot come back) X dx.46. Evaluate the definite integral (3x² - 4x - 5)² (6x-4) dx. 81 215 7 135 3 173 6 8 47. Evaluate the definite integral (4x + 1)³ 4dx. a. 945 c. 2,345 b. 1,320 d. 1,640 48. Approximate the area beneath the curve y = x² + 1 and above the x-axis from x = 0 to x = 4 by using the Left Reimann Sum. Use n = 4. a. 11 square units c. 24 square units b. 18 square units d. 16 square units 49. Refer to the previous item. Solve the same problem but this time by using the Right Riemann Sum. a. 28 square units c. 64 square units b. 19 square units d. 15 square units 50. Find the area bounded by y=x²-4 and y = x + 2. a 42.912 c. 67.983 d. 20.833 b. 34.643 a. b d.
- Assessment Technique: Direction: Evaluate the following integrals. 1. S( 30x5 + 25x3 20x4 dx 3 4 8x5 2. S 15 dx 5 12x3 15 12 3. S 3Il-Find the following integrals by suitable substitutions - |x. (9+ x2))18 dx 1- 2-f, 2xVx2 + 10.dx36 Use substitution to find the indefinite integral dx. (6x-7) 36 dx = 7 (6x - 7)
- Part 1. Evaluate the following Indefinite Integrals (if possible): sec20 do 1. J (tan29 +1)2 dx x3 Vx2 -9 x3 dx 3. V1-x3 4. sec2xdxFind the indefinite integral for the function using the substitution u - X √s 8x² + 7. -dx + 7 S X -dx √ex 8x +7f(t) to simplify For each of the following integrals find an appropriate trigonometric substitution of the form x = the integral. (3x² - а. dx 4x2 + 8 b. x = с. xV 8x2 + 32x + 29 dx dx -45 — За2 — 24х d. x =