How would you integrate something like

sqrt(9-y)*y dy from 0 to 9

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- Sep 6th 2012, 01:42 PMCoffeeBirdHow to integrate this problem
How would you integrate something like

sqrt(9-y)*y dy from 0 to 9 - Sep 6th 2012, 01:51 PMHallsofIvyRe: How to integrate this problem
The problem is that "9- y" inside the square root, right? So try u= 9- y. Then du= -dy. and, of course, y= 9- u. When y= 0, u= 9 and when y= 9, u= 0.

So the and the integral will be from 9 to 0. Swapping the limits of integration gets rid of that negative. - Sep 6th 2012, 02:09 PMCoffeeBirdRe: How to integrate this problem
wow, that was very clearly explained, thank you

- Sep 6th 2012, 03:46 PMSorobanRe: How to integrate this problem
Hello, CoffeeBird!

Quote:

If the expression under the radical is,*linear*

. . we can let equal the entire radical.

Let

Substitute: .

. . . . . . . .

Back-substitute: .

Evaluate: .

. . . . . . . .