Final answer:
The integral of x^5 from 0 to 27 is found by evaluating the antiderivative (1/6)x^6 at the limits of integration and subtracting the results, yielding a large numerical value.
Step-by-step explanation:
To evaluate the given integral ∠0273x5dx, we will apply the fundamental theorem of calculus, which involves finding the antiderivative of the integrand, in this case, the function f(x) = x5. The antiderivative of x5 is ⅖x6 + C, where C represents the constant of integration.
The next step is to evaluate this antiderivative at the upper and lower limits of the integral and subtract the two. So we compute ⅖(27)6 - ⅖(0)6. After calculating, we find that ⅖(27)6 = ⅖(276) = ⅖(318), since 27 is 33, and raising it to the 6th power multiplies the exponents.
Since 318 is a large number, you would typically use a calculator to find the precise value. The integral from 0 to 27 of x5dx is then this large value divided by 6. The resulting value is the definite integral we seek.