Nerd10 said:Homework Statement
Find the integral of (x-4)/x^2 dx from 1 to 2.Homework Equations
Do I divide the denominator? I got 1/x-4/x^2 from 1 to 2. But what to do next?The Attempt at a Solution
The answer is ln(2)-2.
Are you able to integrate 1/x^2 ? If so, then multiply the result by -4 and you'll have this problem half-solved.Nerd10 said:I got 1/x-4/x^2 from 1 to 2. But what to do next
The formula for finding the integral of (x-4)/x^2 from 1 to 2 is ∫[(x-4)/x^2]dx = -1/x + 4ln|x| from 1 to 2.
To solve the integral of (x-4)/x^2 from 1 to 2, you can use the formula ∫[(x-4)/x^2]dx = -1/x + 4ln|x| and plug in the values of 1 and 2 to get the final answer.
First, use the formula ∫[(x-4)/x^2]dx = -1/x + 4ln|x|. Then, substitute the limits of 1 and 2 into the formula. Finally, solve for the final answer by plugging in the values and simplifying.
The integral of (x-4)/x^2 from 1 to 2 represents the area under the curve of the function (x-4)/x^2 between the limits of 1 and 2. It is a useful tool in calculating the total change or accumulation of a quantity over a given interval.
Yes, the integral of (x-4)/x^2 from 1 to 2 has many real-life applications, such as in physics to calculate the displacement of an object given its velocity function, or in economics to determine the total cost or revenue of a business over a specific time period.