find the area between the curve y= 1 divided by (1=3x)^2
To find the area between the curve y = 1/(1-3x)^2, we need to integrate the function with respect to x over the desired interval.
Step 1: Find the bounds of the interval.
The given equation does not specify the bounds of the interval. We'll assume you want to find the area between the curve for a specific interval, such as [a, b].
Step 2: Integrate the function.
To find the area, we integrate the given function with respect to x over the interval [a, b]. The integral of 1/(1-3x)^2 is:
∫(1/(1-3x)^2) dx
Step 3: Evaluate the definite integral.
Plug in the upper bound, b, and lower bound, a, into the integral expression from Step 2. Then subtract the result from evaluating the integral with the lower bound from evaluating the integral with the upper bound. This will give you the area between the curve over the given interval.
Area = ∫(1/(1-3x)^2) dx evaluated from a to b
= ∫(1/(1-3x)^2) dx │[a, b]
= ∫(1/(1-3x)^2) dx │[a, b] - ∫(1/(1-3x)^2) dx │[a, b]
To find the exact values of the definite integral, you'll have to evaluate the antiderivative of 1/(1-3x)^2 and substitute the upper and lower bounds into the expression.
Please provide the specific interval [a, b] to proceed with the calculations.