Question

Question about integral

Answer 1

\[\large \int\limits_{-3}^{4}(1+\sqrt{9-x^2}) ~dx\]
How do I do this one?

Answer 2

@jim_thompson5910

Answer 3

@3mar

Answer 4

This integral is not possible right?

Answer 5

why?

Answer 6

first break the integral up

\[\large \int\limits_{-3}^{4}(1+\sqrt{9-x^2}) ~dx =\int\limits_{-3}^{4}(1) ~dx + \int\limits_{-3}^{4}(\sqrt{9-x^2}) ~dx\]

Answer 7

the first part is fairly straight forward

the second one will require a trig sub, see the link
http://calculus.nipissingu.ca/tutorials/integralgifs/trig_sub_table.gif

Answer 8

Take the lead, @jim_thompson5910

Answer 9

I haven't learned about trig subs yet, and I think I am supposed to solve this with graphing since \[\large \sqrt{9-x^2}\] will be a semicircle

Answer 10

if you go from x = -3 to x = 3, then yes it's a semicircle

any value of x such that x > 3 will not produce a real number result

eg: x = 4

sqrt(9-x^2) = sqrt(9-4^2) = sqrt(9-16) = sqrt(-7) = i*sqrt(7)