Evaluate the integrals in Exercises 67–74 in terms of
b....

Question

Evaluate the integrals in Exercises 67–74 in terms of

b. natural logarithms.

69. ∫(from 5/4 to 2)dx/(1-x²)

Accepted Answer

Welcome back everyone. Evaluate the integral from 0 to 1 of D X divided by X2 + 2 X + 1. Aces 3 halves, B 1/22, C1 and D2. For this problem we're going to use use substitution, but before we begin, let's notice that in the denominator we have x2 + 2 x + 1, which is a perfect square. It is equal to x + 12. So what we can do is set u equal to x + 1. And remember that the next step is to find the derivative of U with respect to X, which is the derivative of X + 1, and that's 1. So essentially, DU is equal to DX according to this relationship, and the next step is to change the limits of integration. So the lower 1 u1 is going to be 0 + 1, which is 1. And the upper limit of integration of U2 is going to be 1 + 1, which is 2. So we can now rewrite the integral in terms of U and DU. We're integrating from 1 up to. 2 d x becomes d u because they are equal to each other, and in the denominator we have u squared. We can rewrite the integral as u to the power of -2. D eu from 1 to 2. And we can integrate using the power rule, so we are going to get you to the power of -1 divided by -1. -1 + 1, I'm sorry, -2 + 1. Gives us -1 and we're dividing by -1. Division by -1 can be replaced with a negative sign in front. U to the power of -1 is. 1 divided by you. And we're going to evaluate the result from 1 to 2. Applying the evaluation theorem, we're going to get -1 divided by. 2, this is our upper limit minus -1 divided by 1, which is the lower limit. of -1 is positive. 1 and we're subtracting 1/2. Which is equal to 1/22 and this corresponds to the answer of choice b. Thank you for watching.

Evaluate the integrals in Exercises 67–74 in terms ofb. natural logarithms.69. ∫(from 5/4 to 2)dx/(1-x²)

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Evaluate the integrals in Exercises 67–74 in terms of
b. natural logarithms.
69. ∫(from 5/4 to 2)dx/(1-x²)