Question

INTEGRATE:

Answer 1

\[Y=10 - t^{3}\]

Answer 2

-3t^2

Answer 3

The rule is:
\(\color{#000000 }{ \displaystyle \int\limits x^n~dx~= \frac{x^{n+1}}{n+1}\color{grey}{\rm +C} }\)

\(\color{#000000 }{ \displaystyle \int\limits a\cdot x^n~dx~= a\cdot \frac{x^{n+1}}{n+1}\color{grey}{\rm +C} }\)

ALSO:
\(\color{#000000 }{ \displaystyle \int\limits a~dx=\int\limits ax^0~=a\times \frac{x^{0+1}}{0+1}\color{grey}{\rm +C}=ax\color{grey}{\rm +C} }\)

Answer 4

@happyrosy integrate, not differentiate!

Answer 5

Oh right! Whoops!

Answer 6

\(\color{#000000 }{ \displaystyle \int(10-t^3)~dt }\)

\(\color{#000000 }{ \displaystyle \int 10~dt - \int t^3~dt }\)

Answer 7

you are just applying the power rule to each term.

Answer 8

can you help me to get the final answer :)

Answer 9

\(\color{#000000 }{ \small \displaystyle \int (12z^3+ 12z^2+12z+12)~dz }\)

\(\color{#000000 }{ \small \displaystyle =12\cdot \frac{z^{3+1}}{3+1}+12\cdot \frac{z^{2+1}}{2+1}+12\cdot \frac{z^{1+1}}{1+1}+12\cdot \frac{z^{0+1}}{0+1}\color{grey}{\rm +C} }\)

\(\color{#000000 }{ \small \displaystyle =12\cdot \frac{z^{4}}{4}+12\cdot \frac{z^{3}}{3}+12\cdot \frac{z^{2}}{2}+12\cdot \frac{z^{1}}{1}\color{grey}{\rm +C} }\)

\(\color{#000000 }{ \small \displaystyle =3z^{4}+4z^{3}+6z^{2}+12z\color{grey}{\rm +C} }\)

Answer 10

that is an example

Answer 11

you always apply that rule, except if the power is -1.

Answer 12

\[-2t ^{4} + C ?\]

Answer 13

\(\color{#000000 }{ \displaystyle t^3=\frac{t^{3+1}}{3+1} }\)

\(\color{#000000 }{ \displaystyle -t^3=-\frac{t^{3+1}}{3+1} }\)

Answer 14

that is the integral.

Answer 15

and the integral of 10?

Answer 16

can you find the integral of 10?

Answer 17

zero

Answer 18

?

Answer 19

@SolomonZelman

Answer 20

The integral of 10 is 10x

Answer 21

final answer is?