Question

Evaluate the integral ∫₀¹ 81t² dt.

Answer 1

To evaluate the integral ∫₀¹ 81t² dt, use the power rule of integration. Apply the rule by adding 1 to the exponent and dividing by the new exponent.

Step-by-step explanation:

To evaluate the integral ∫01 81t² dt, we can use the power rule of integration. The power rule states that for any constant exponent n, the integral of x^n dx is equal to (x^(n+1))/(n+1), plus a constant of integration.

In this case, we have the integral ∫01 81t² dt. Applying the power rule, we add 1 to the exponent and divide by the new exponent:

∫01 81t² dt = (81t³/3) evaluated from 0 to 1 = (81/3) - (0/3) = 27 - 0 = 27.