Question

Find ∫
5
(5𝑥−1)
2 𝑑𝑥 2
1

Answer 1

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

Answer 2

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

Answer 3

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.

Answer 4

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.

Answer 5

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.