Question

help setting this up...?

Answer 1

\[\int\limits_{0}^{\pi} (5e^x+3sinx)dx\]

Answer 2

I got
....+(3sinx^2/2) but im stuck

Answer 3

integrating sin doesn't give you sin^2

Answer 4

The rule you tried to apply there works only for polynomials. You want to a function whose derivative is 3 sin x. And another function whose derivative is 5 e^x.

Answer 5

3cosx?

Answer 6

then what do i do for this one..?

Answer 7

-3 cos x

Answer 8

d/dx cos x = - sin x.

Answer 9

yeah i forgot the negative.. sorry

Answer 10

d/dx e^x = e^x.

Answer 11

e^x is special in that regard. It's the only function with that property.

Answer 12

so it stays the same... (5e^(x)-3cosx and the i just do F(b)-F(a)

Answer 13

Yep. That's the fundamental theorem of calculus.

Answer 14

Since you've got a pi as one boundary of the interval you're integrating over, you might end up with some things that you'll have to either leave as a symbol, like e^pi, or you'll get a decimal approximation because it'll be irrational.

Answer 15

yeah i got... -116.7034632

Answer 16

Yeah. You should get a definite rational number for -3 cos pi. But Then I would leave e^pi in its symbolic form, probably... up to you.

Answer 17

-1-5e^pi ... thank you!!