Question

Calculus 2 - Antiderivatives

Answer 1

\(Q'(y) = q(y)\)

integrate both sides

\(Q(y) = \int q(y) dy = \int y^8 + \frac{1}{y} dy \)

Answer 2

1/9*y^9 + lny? that was wrong

Answer 3

no take the derivative to see if u have y^8 + 1/y in return

Answer 4

if u do, you did it right

Answer 5

ln y +y^9/9 ?

Answer 6

thats right, but u need to add a constant whenever u take integral

Answer 7

oh yeah forgot X<>X

Answer 8

\(\large Q(y) = \int q(y) dy = \int y^8 + \frac{1}{y} dy = \frac{y^9}{9} + \ln |y| + c \)

Answer 9

find the constant \(c\), and plugin above

Answer 10

we're given : \(Q(1) = 1/9\)

plugin \(y = 1\) below and solve \(c\):-

\(\large Q(y) = \frac{y^9}{9} + \ln y + c\)

Answer 11

1/9 = c?

Answer 12

\(\large Q(1) = \frac{1}{9} + \ln 1 + c = \frac{1}{9} + c\)

\(\large \frac{1}{9} = \frac{1}{9} + c\)

\(0 =c\)

Answer 13

ok so y^9/9+ln|y| is answer?

Answer 14

yes

Answer 15

ty

Answer 16

np :) this time it accpeted ha ?

Answer 17

yes :)

Answer 18

good :)