Final answer:
To find the integral that is equal to 5/4, we need to evaluate each given integral. The integral that is equal to 5/4 is option b. ∫¹₀ 1/x⁰.⁵ dx.
Step-by-step explanation:
To find the integral that is equal to 5/4, we need to evaluate each given integral. Let's go through each option:
a. ∫¹₀ 1/x⁰.² dx = ∫¹₀ 1/x dx = ln|x| | from 1 to 10 = ln(10) - ln(1) = ln(10)
b. ∫¹₀ 1/x⁰.⁵ dx = ∫¹₀ x^(-0.5) dx = 2x^(0.5) | from 1 to 10 = 2(10^0.5) - 2(1^0.5) = 2√10 - 2
c. ∫¹₀ 1/x⁰.⁷ dx = ∫¹₀ x^(-0.7) dx = 10^(0.3) - 1^(0.3) = √10 - 1
d. ∫¹₀ 1/x² dx = -1/x | from 1 to 10 = -1/10 - (-1/1) = -1/10 + 1 = 9/10
Therefore, the integral that is equal to 5/4 is option b. ∫¹₀ 1/x⁰.⁵ dx.