Question

Find the exact value of the area between the graph of y = cosx and y = e^x for 0 ≤ x ≤ 1.

Answer 1

i know that the antiderivative of cos(x) is sin(x) and the antiderivative of e^x is e^x and since the interval is from 0 to 1 i know that i would do cos(1)-cos(0)= some value and then e^1-e^0=some value, but its asking for an EXACT answer so idk what to put. I write down a decimal and it says its wrong :/

Answer 2

ok so we do \[\int\limits_{0}^{1}(e^x-\cos(x))dx \]

Answer 3

why do you plug in 1 in limits into the cos function

Answer 4

you plug in limits into the antiderivative

Answer 5

not the original function

Answer 6

oh yeah sorry thats my mistake i meant sin (x)

Answer 7

so its e^x-sinx

Answer 8

so what do you get after integrating that e^x-sin(x) is correct
so plug in your limits

Answer 9

so i plug in e^1-sin(0)=2.718281828

Answer 10

(e^1-sin(1))-(e^0-sin(0))
e^1-sin(1)-1+0
e-sin(1)-1<---this is exact answer

Answer 11

ohhhh i see what i was doing wrong

Answer 12

thank you!!!

Answer 13

you were letting e^0 =0?

Answer 14

a^0 =1
excluding when a=0

Answer 15

yeah idk what i was doing; i always make those kinds of mistakes