Question

It is given that:

Answer 1

\[\int\limits_{0}^{a} (\frac{ 1 }{ 2 }e^{3x} +x^2) dx = 10 \]

Answer 2

Show that \[a = \frac{ 1 }{ 3 }\ln(61-2a^3)\]

Answer 3

@518nad

Answer 4

okay

Answer 5

integration is linear so u can integrate one term at a time

Answer 6

Okay, one second.

Answer 7

I forgot how to do the e part, actually.

Answer 8

okay so remember e^x is sepcial because d/dx e^x = e^x
and therefore int e^x dx = e^x

Answer 9

d/dx e^3x = (3x)' e^(3x) = 3*e^3x
by chain rule,

so you know that
integral of 3*e^3x = e^3x
very close to what we got
this means integral of e^3x = 1/3 e^3x

Answer 10

So it should be (e^3x)/6? or 1/6 e^3x (same thing)

Answer 11

yes

Answer 12

\[\int\limits_{?}^{?} (e ^{3x})/(6) + \int\limits_{?}^{?} (x^3)/(3)\]