Question

STUCK! How do you evaluate this?

Answer 1

\[\int\limits_{0}^{1}4dx + \int\limits_{0}^{1} 3x^2 dx\]

Answer 2

\[=\int\limits_{0}^{1} 4 dx + 3 \int\limits_{0}^{1}x^2 dx\]

Answer 3

= \[=4(0-1) + 3\int\limits_{0}^{1}x^2 dx\]

Answer 4

Now I'm stuck. ;/

Answer 5

it'll be 4(1-0) for the first integral. always plug in top - bottom
to integrate x^2, just follow the same process; add 1 to the exponent and then divide the term by the new exponent's number

Answer 6

@notshh just said, in words: \(\int x^k dx = \frac{x^{k+1}}{k+1}\).
Therefore, \[
\int_0^1 x^k dx = \left[\frac{x^{k+1}}{k+1}\right]_0^1.
\]

Answer 7

oops yes I meant 4(a-b) lol

Answer 8

4(b-a) ***

Answer 9

so now it's 4+3*(x^3)/3

Answer 10

yup. all you need to do now is evaluate the integral and simplify

Answer 11

I don't understand lol, we've only been learning how to solve the area under a curve now all the sudden we have to integrate?