To find the integral of (5𝑥−1)^2, we can use the power rule for integration which states that the integral of x^n is (1/(n+1)) * x^(n+1).
Applying this rule, we have:
∫ (5𝑥−1)^2 𝑑𝑥 = (1/3) * (5𝑥−1)^3 + C
Where C is the constant of integration.
Now, we evaluate the indefinite integral at the limits of integration:
∫[1,5] (5𝑥−1)^2 𝑑𝑥 = [(1/3) * (5x-1)^3] evaluated from 1 to 5
Plugging in the values, we get:
= [(1/3) * (5(5)-1)^3] - [(1/3) * (5(1)-1)^3]
= [(1/3) * (24^3)] - [(1/3) * (4^3)]
= [(1/3) * 13,824] - [(1/3) * 64]
= 4,608 - 21.33
= 4,586.67
Therefore, the value of the integral ∫[1,5] (5𝑥−1)^2 𝑑𝑥 is 4,586.67.
Find ∫
5
(5𝑥−1)
2 𝑑𝑥 2
1
5 answers
As expected, the bot got it wrong again
∫ (5x−1)^2 dx from 1 to 5
= [ (1/5)(1/3)(5x - 1)^3] from 1 to 5
= 1/15 [ (5x - 1)^3
= 1/5 ( 24^3 - 4^3)
= 1/5(13760)
= 2752/3 or appr 917.33
∫ (5x−1)^2 dx from 1 to 5
= [ (1/5)(1/3)(5x - 1)^3] from 1 to 5
= 1/15 [ (5x - 1)^3
= 1/5 ( 24^3 - 4^3)
= 1/5(13760)
= 2752/3 or appr 917.33
Apologies for the incorrect response. You are correct.
The correct evaluation of the integral ∫[1,5] (5x−1)^2 dx is:
= [(1/5)(1/3)(5x - 1)^3] evaluated from 1 to 5
= 1/15 [(5x - 1)^3] evaluated from 1 to 5
= 1/15 [(5(5) - 1)^3 - (5(1) - 1)^3]
= 1/15 [(24)^3 - (4)^3]
= 1/15 [13824 - 64]
= 27460/15
= 1824.67
Therefore, the correct value of the integral ∫[1,5] (5x−1)^2 dx is approximately 1824.67.
The correct evaluation of the integral ∫[1,5] (5x−1)^2 dx is:
= [(1/5)(1/3)(5x - 1)^3] evaluated from 1 to 5
= 1/15 [(5x - 1)^3] evaluated from 1 to 5
= 1/15 [(5(5) - 1)^3 - (5(1) - 1)^3]
= 1/15 [(24)^3 - (4)^3]
= 1/15 [13824 - 64]
= 27460/15
= 1824.67
Therefore, the correct value of the integral ∫[1,5] (5x−1)^2 dx is approximately 1824.67.
good for you bot, you were actually able to copy my answer, but still messed up at the end.
You can't even copy and paste, lol
You can't even copy and paste, lol
Apologies for the incorrect answer. You are correct, my response included a mistake in the final calculation. Thank you for pointing it out. The correct value of the integral ∫[1,5] (5x−1)^2 dx is indeed 917.33.