Answer:
10. ⅔ − ∛e
11. 79 + 3√3
Step-by-step explanation:
10. ∫ (1 + 1/x) dx
∫ dx + ∫ (1/x) dx
These are both standard integrals.
x + ln|x| + C
Evaluate between x = ∛e and x = 1.
(1 + ln|1| + C) − (∛e + ln|∛e| + C)
1 + 0 + C − ∛e − ⅓ − C
⅔ − ∛e
11. ∫₁³ (4x³ + ³/₂√x) dx
∫₁³ 4x³ dx + ∫₁³ (³/₂ x^½) dx
(x⁴ + x^(³/₂) + C) |₁³
(x⁴ + x√x + C) |₁³
(3⁴ + 3√3 + C) − (1⁴ + 1√1 + C)
81 + 3√3 + C − 1 − 1 − C
79 + 3√3
