Step-by-step explanation:
In this case we have:
Δx = 3/n
b − a = 3
a = 1
b = 4
So the integral is:
∫₁⁴ √x dx
To evaluate the integral, we write the radical as an exponent.
∫₁⁴ x^½ dx
= ⅔ x^³/₂ + C |₁⁴
= (⅔ 4^³/₂ + C) − (⅔ 1^³/₂ + C)
= ⅔ (8) + C − ⅔ − C
= 14/3
If ∫₁⁴ f(x) dx = e⁴ − e, then:
∫₁⁴ (2f(x) − 1) dx
= 2 ∫₁⁴ f(x) dx − ∫₁⁴ dx
= 2 (e⁴ − e) − (x + C) |₁⁴
= 2e⁴ − 2e − 3
∫ sec²(x/k) dx
k ∫ 1/k sec²(x/k) dx
k tan(x/k) + C
Evaluating between x=0 and x=π/2:
k tan(π/(2k)) + C − (k tan(0) + C)
k tan(π/(2k))
Setting this equal to k:
k tan(π/(2k)) = k
tan(π/(2k)) = 1
π/(2k) = π/4
1/(2k) = 1/4
2k = 4
k = 2
Answer:
Step-by-step explanation:
Tbh I haven’t learned this
Answer:
Step-by-step explanation:
Given
Required
Express in different ways
The first way is:
Subtract 2 from both sides
------ (1)
Another way is:
Subtract 3 from both sides
--- (2)
Distance between T(80, 20) and U(20, 60) = sqrt((20 - 80)^2 + (60 - 20)^2) = sqrt((-60)^2 + (40)^2) = sqrt(3600 + 1600) = sqrt(5200) = 72.11 units
Distance between T(80, 20) and V(110, 85) = sqrt((110 - 80)^2 + (85 - 20)^2) = sqrt((30)^2 + (65)^2) = sqrt(900 + 4225) = sqrt(5125) = 71.59
Distance between U(20, 60) and V(110, 85) = sqrt((110 - 20)^2 + (85 - 60)^2) = sqrt((90)^2 + (25)^2) = sqrt(8100 + 625) = sqrt(8725) = 93.41
Therefore, shortest distance for the trip = 71.59 + 93.41 = 165 units.
Answer:
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Step-by-step explanation:
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