Evaluate the definite integral. Use a graphing utility to verify your result.54x3x − 4 dx

It seems like there might be a typo in your integral. The expression "54x3x - 4 dx" is not properly formatted for an integral.

If you meant ∫(54x^3 - 4) dx, here's how you would solve it:

Step 1: Find the antiderivative of the function. The antiderivative of x^n is (1/(n+1))x^(n+1), and the antiderivative of a constant is just the constant times x. So, the antiderivative of 54x^3 - 4 is (54/4)x^4 - 4x.

Step 2: Since this is a definite integral, you would then subtract the antiderivative evaluated at the lower limit of integration from the antiderivative evaluated at the upper limit of integration. However, you didn't provide limits of integration, so I can't complete this step.

As for verifying the result with a graphing utility, you would graph the original function and the antiderivative function on the same set of axes. The area between the two curves from the lower limit of integration to the upper limit of integration should be equal to the value of the definite integral.

Please provide the limits of integration so I can give a complete answer.