Final answer:
To find the area under the curve y=9x over the interval [1,5], we compute the definite integral and find the area to be 108, which is not listed in the given options.
Step-by-step explanation:
The task is to find the area under the curve y=9x over the interval [1,5]. This problem falls under the category of integral calculus. We can approach this problem by calculating the definite integral of the function from x=1 to x=5. Mathematically, we would write this as the integral from 1 to 5 of 9x dx. The antiderivative of 9x is ½(9x^2), and applying the fundamental theorem of calculus, we evaluate this antiderivative at the upper and lower bounds of the interval.
Let's solve the mathematical problem completely:
Calculate the antiderivative: ½(9x^2) = ¾(3x)^2
Evaluate at x=5: ½(9*5^2) = ½(9*25) = ½(225) = 112.5
Evaluate at x=1: ½(9*1^2) = ½(9) = 4.5
Find the difference: 112.5 - 4.5 = 108
The result of calculating the definite integral from x=1 to x=5 for the function y=9x is 108, which corresponds to the area under the curve for this interval. It appears that the options provided do not include the correct answer and thus there might be a mistake in the problem statement or the options given.