Question

Amistre64 can you help me?

Answer 1

\[\int\limits_{}^{}15/2(t+1)^{1/2}\]

Answer 2

we can do this

Answer 3

\[\int\frac{15}{2\sqrt{t+1}}dt\]?

Answer 4

can someone help me?

Answer 5

is that the question? first off the constants come right out front of the integral sign

Answer 6

yes that is the question and thank you

Answer 7

\[\frac{15}{2}\int \frac{1}{(t+1)^{\frac{1}{2}}}\]

Answer 8

now a very simple u - substitution, not even really necessary. put
\[u=t+1\] and
\[du=dt\] so you get
\[\frac{15}{2}\int u^{-\frac{1}{2}}du\]

Answer 9

now use power rule backwards to get the anti - derivative

Answer 10

\[\int u^{-\frac{1}{2}}=2u^{\frac{1}{2}}\]

Answer 11

hope that is clear. just add one to the exponent and then divide by that exponent.

Answer 12

yesthat is clear

Answer 13

now replace u by t +1 and remember there is a fraction out front to get
\[\frac{15}{2}\times 2 (t+1)^\frac{1}{2}=15\sqrt{t+1}\]

Answer 14

and i guess you need that stupid +C at the end

Answer 15

easy check is to take the derivative and see that you have it correct.

Answer 16

yes you need that stupid C

Answer 17

ok hope all steps are clear. little practice with ones like this you do the "u substitution" in your head since in this case du = dx

Answer 18

btw ictrees sent me to you. she is incognito