Question

Evaluate the integral ∫(x2 + 4x -2)dx from x = 1 to x = 4.

Answer 1

A. 16
B. 25
C.45
D. 49

Answer 2

Integrate it first

Answer 3

what does that mean?

Answer 4

You don't know what integrate means? ._.

Answer 5

......no. im not good at this stuff

Answer 6

\( \int x^n dn = \dfrac{x^{n + 1}}{n+1} + C \)

Answer 7

It means work backwards to the original equation. But looks like mathstudent is cooking something up, so I'll wait~

Answer 8

Integration is the opposite of differentiation.
If you start with a function and you integrate it you get a new function.
If you differentiate the new function, you get your original function back.

Answer 9

so i just plug everything in?

Answer 10

and if so, what is n?

Answer 11

For example:

\( \int (x^2 + 3x + 1)dx = \dfrac{x^3}{3} + \dfrac{3x^2}{2} + x + C\)

Now differentiate the new function:

\( \dfrac{d}{dx} (\dfrac{x^3}{3} + \dfrac{3x^2}{2} + x + C) \) =

\(= \dfrac{3x^2}{3} + \dfrac{6x}{2} + 1\)

\(= x^2 + 3x + 1\)

As you can see, when you integrate and differentiate, you get back to the same starting point.

Answer 12

Follow the integration part of my example.

Answer 13

how did u get 3 and 2 as denominators?

Answer 14

Look at the formula for integrating x^n:

\(\int x^n dn = \dfrac{x^{n + 1}}{n+1} + C\)