Question

CALCULUS I | Evaluate the following integrals by interpreting in terms of areas (geometric approach)

Answer 1

\[\int_{-1}^{4}(2x-1)dx\]\[\int_{0}^{4}(2-\sqrt{16-x^2})dx\]

Answer 2

I suggest graphing them if you're unfamiliar with what these shapes are so that you can recognize them in the future.

Answer 3

#1: finished. I need answer checks.
#2: I cannot graph it properly. Should I split up the integral?

Answer 4

Yeah you can split up the integral that's a good idea, then just add up the area of the pieces

Answer 5

I think specifically this might be the hardest part to recognize, but if you know the area of this from before calculus you'll be set.

Answer 6

My professor said not to, and mentioned something about a quarter circle. I assume that is the second half, but I cannot figure out how to do it without this --\[\int{f(a)}-\int{f(b)}\]

Answer 7

For the second one

y=2-sqrt{16-x^2}

(y-2)^2=16-x^2

Try converting this equation into standard form of circle and find its radius and center
Its graph will be a semicircle

Answer 8

What do you mean you were told this? Graph it to see it for yourself.

Answer 9

If you can't graph it, now's the time to learn

Answer 10

it will be a quarter circle for x=0 to x=4

Answer 11

and that splitting up integrals was unnecessary...

Oh, I see. Thank you @Salty

Answer 12

Yw