Use the table of integrals at the back of the text to evaluate...

Question

Use the table of integrals at the back of the text to evaluate the integrals in Exercises 1–26.

∫ √(x - x²) / x dx

Accepted Answer

Welcome back, everyone. Using a standard inaugural table, evaluate the following indefinite integral. We have integral of square root of 4 X minus X2 divided by XD X. What we can notice is that the given integral has a form of. Integral square root of. 2 A X minus X squared divided by XD X. Where A is a number, right? And specifically by analogy, we can notice that 2A is basically a constant in front of X, and that's 4. So now, if we know the formula, we can solve this integral. And according to the tables of integrals, well, we can essentially get a formula for this type of integral as follows. We're going to take square root of 2 A X minus X2d, so we're taking our numerator and we're going to add a multiplied by inverse of sign. Of x minus a divided by A And we're going to add the constant of integration C because this is an indefinite integral. So by analogy, we can now show that 2A is equal to 4 in our case, meaning A is equal to 4 divided by 2, which is 2. So now we are ready to evaluate the integral. Using the formula, we are going to get square root off. 2 A X, so that's 2 multiplied by 2 multiplied by X, that's simply 4 X minus X squared. And we're going to add a, which is 2, multiplied by inverts of sine of X minus A, that's X minus 2, divided by A, which is 2, plus C. That's how we have got our final answer. Thank you for watching.

Use the table of integrals at the back of the text to evaluate the integrals in Exercises 1–26.∫ √(x - x²) / x dx

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Use the table of integrals at the back of the text to evaluate the integrals in Exercises 1–26.
∫ √(x - x²) / x dx