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1. For the integral from 4 to 4 point 5 of 3 divided by square

root of quantity negative 15 plus 8 x minus x squared end quantity

times dx Part A: Determine if long division will be used for this

integration and justify your answer. (5 points) Part B: Simplify

the integrand and use a u substitution to rewrite the integral with

new limits of integration. (15 points) Part C: Evaluate the

integral. Round to the nearest thousandth. (10 points)

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Transcript

for this problem we are to evaluate the definite integral from 4 to 4.5 of three over the square root of negative 15 plus eight x minus x squared dx. Now, for the first part we want to determine if long division is necessary in order to simplify the integral. Now, since the integration is not a rational expression, then the long division is not necessary. And now for part B we have to simplify the inter grand. To simplify, we have to apply completing the square to the inside of the squared in the denominator. Now negative 15 plus eight X minus x squared is equal to negative of x squared -8 X -15. That’s negative of x squared minus eight X plus 16 plus one Which becomes 1- the square of X -4. So we can rewrite the integral and…

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