How do you do this question?

∫₂⁵ ln(x) dx

Step-by-step explanation:

lim(n→∞) ∑ᵢ₌₁ⁿ (3/n) ln((2n + 3i) / n)

lim(n→∞) ∑ᵢ₌₁ⁿ (3/n) ln(2 + (3/n) i)

The width of the interval is b−a = 3, and there are n rectangles.  So the width of each rectangle is 3/n, and the height of each rectangle is ln(2 + (3/n) i).

The ith term is 2 + (3/n) i, so a = x₀ = 2.  Therefore, b = 2+3 = 5.

So the region is the area under f(x) = ln(x) between x=2 and x=5.

∫₂⁵ ln(x) dx

7. d. 64

8. i. 32

9. c. 125

10. j. none of the above

11. d. 81

12. i. 216

13. e. none of the above

14. g. 240

15. e. none of the above

16. g. 32

17.   e. none of the above

the answer to this question is 3/19

step-by-step explanation: