Question

it is estimated that the number of residents of a certain city who seek employment during the period of t years is W(x)= integral 500,000/(3sqrt(x^2-6x+10))dx people. find the number of people who are seeking employment in the next 10 years

Answer 1

\[\int\limits_{0}^{t}500000/(3 \sqrt{x^2-6x+10})dx\]

Answer 2

i think i have to complete the square?

Answer 3

it's pretty much done for you, just split it up:\[\sqrt{x^2-6x+9+1}=\sqrt{(x-3)^2+1}\]\[\tan\theta=x-3\to\sec^2\theta d\theta=dx\]

Answer 4

\[\frac{5\times10^5}{3}\int\frac{dx}{\sqrt{(x-3)^2+1}}=\frac{5\times10^5}{3}\int\frac{\sec^2\theta d\theta}{\sqrt{\tan^2\theta+1}}\]you've done it from here with myin, same deal

Answer 5

yup! thanks

Answer 6

here's the triangle for you
welcome :D