Question

Need help with definite integrals

Answer 1

I find these confusing because I have to find the definite integrals for
\[f \prime(x) dx\]

Answer 2

sorry I had to attach a file but you need to look at the graph

Answer 3

I need someone to double check my solutions
33. is 3
34 is 4 but I am not sure on this one
35 is 8/3

Answer 4

I found the slope of each line segment and then I calculate the dx of line segment

Answer 5

Can someone double check my solutions?

Answer 6

slope from (-4,-3) to (-1,-2) is 1/3
slope from (-1,-2) to (1,2) is 2
slope from (1, 2) to (3,-2) is -2

Answer 7

33 and 34 are correct
35 is wrong

Answer 8

an easier way is to use the fundamental theorem of calculus :

\(\int_a^b f'(x) = f(b) - f(a)\)

Answer 9

for 33 :

\(\int_{-4}^0 f'(x) = f(0) - f(-4) = 0 - (-3) = 3\)

Answer 10

for 34 :

\(\int_{-1}^1 f'(x) = f(1) - f(-1) = 2 - (-2) = 4\)

Answer 11

I still got 8/3 using FTC

Answer 12

for 35

Answer 13

f(2) = 0
f(-3) = -8/3
0-(8/3) =8/3

Answer 14

oh yes ! i made a mistake you're right !

Answer 15

No problem. Thank you, I would not have thought to use FTC in the first place

Answer 16

good to know both ways :)

Answer 17

yes I agree