Question

definite integral of x+3 lower limit -1 upper limit 3. Step by step please

Answer 1

hi
\[\int\limits_{-1}^3(x+3)\;\mathrm dx
=\frac{x^{1+1}}{1+1}+3\frac{x^{0+1}}{0+1}\Big|_{-1}^3\]

Answer 2

does this step make sense,?

each term in the integrand has had its index of x raised by one, and then that term is divided by the new index

Answer 3

Hello, yes so far it makes sense.

Answer 4

@UnkleRhaukus

Answer 5

so now simplify those denominators and indexes , what do you get ?

Answer 6

\[\frac{ 1 }{ 2 }(x^2+3)\]

Answer 7

opps 3x

Answer 8

check the denominator of that second term

Answer 9

\[\frac{ 1 }{ 2 }(x^2+3x)\]

Answer 10

almost, but not quite

Answer 11

1+0=1≠2

Answer 12

\[\frac{ x^2 }{ 2 }+3x\]

Answer 13

that is better!

so you have

\[\int\limits_{-1}^3(x+3)\;\mathrm dx
=\frac12x^2+3x\Big|_{-1}^3\]

now to evaluate the limits
\[=\Big(\tfrac12(3)^2+3(3)\Big)-\Big(\tfrac12(-1)^2+3(-1)\Big)\]

Answer 14

So the final answer will be 16?

Answer 15

\[\large\color{red}\checkmark\]

Answer 16

Thanks!(: