Evaluate the integrals in Exercises 53–76.
59. ∫(from 0 ...

Question

Evaluate the integrals in Exercises 53–76.

59. ∫(from 0 to 1)4ds/√(4-s²)

Accepted Answer

Welcome back everyone. Evaluate the definite integral from 0 to 2 of 3 d x divided by the square root of 9 minus x 2. For this problem, let's begin by applying the properties of integrals. We can rewrite it as the integral from 0 to 2. We can factor out 3 because it's a constant, and we're going to integrate the x divided by square root of 9 minus x 2. And this is the variation of elementary integrals. Let's remember that the integral of d x divided by the square root of a 2 minus x2 is equal to inverse of sin of x divided by a plus a constant of integration c. So in this case 9 can be written as 32 and therefore a is equal to 3, right? So we first will get 3, which is our constant, followed by inverse of sin of x divided by a, and we already know that a is equal to 3. There is no necessity to add C because we have a definite integral, we just want to evaluate the result from 0 to 2. Which is going to be equal to 3 inverts of sin of. 2 divided by 3. -3 inverse of sin of 0 divided by 3 witches 0. And because inverse of sin of zero is 0, we can just cross out the final term, and this is how we get our final answer, which is 3 inverse of sin. Of 2/3 Thank you for watching.

Evaluate the integrals in Exercises 53–76.59. ∫(from 0 to 1)4ds/√(4-s²)

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Evaluate the integrals in Exercises 53–76.
59. ∫(from 0 to 1)4ds/√(4-s²)