Evaluate the following integral using trigonometric substitution Integral underroot dx/ 9-x^2

The result of the integral is:

Step-by-step explanation:

We are given the following integral:

Trigonometric substitution:

We have the term in the following format: , in which a = 3.

In this case, the substitution is given by:

So

In this question:

So

We have the following trigonometric identity:

So

Replacing into the integral:

Coming back to x:

We have that:

So

Applying the arcsine(inverse sine) function to both sides, we get that:

The result of the integral is:

the answer is (4,3)

since the rule for r0, 90º is (-y,x) and it was already applied to form the image, all you have to do is reverse the answer using this formula.

f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50