Final answer:
To find the area under the curve y = 13x^3 from x = 1 to x = t, we can use integration. Evaluating the area under the curve for t = 10, t = 100, and t = 1,000 gives us the respective areas of approximately 43,437.5, 4,343,750, and 43,437,500 square units.
Step-by-step explanation:
The question asks for the area under the curve y = 13x^3 from x = 1 to x = t. To find the area under the curve, we can use integration. The definite integral of 13x^3 from 1 to t gives us the area under the curve between these x-values.
To evaluate the area under the curve for different values of t, we substitute t into the integral expression and calculate the result. For t = 10, t = 100, and t = 1,000, we plug these values into the integral and solve to find the respective areas under the curve.
For t = 10: The area under the curve is approximately 43,437.5 square units.
For t = 100: The area under the curve is approximately 4,343,750 square units.
For t = 1,000: The area under the curve is approximately 43,437,500 square units.