Intergration (can someone work out)

**cjdyer** · June 8th 2010, 03:28 AM

i would greatly appreciate if someone could work these out for me, because im struggling and need some examples on how to intergrate

bold letter are powers!

y = 3x6

y = 4x4 +3

y = (5-3x)2

Y = 5 sin 2x

Y = cos 1 x
3

Y = 1 + √x
x

Y = e 3x + 7
e x

**pickslides** · June 8th 2010, 03:33 AM

Some rules to help you.

$\int x^n~dx = \frac{x^{n+1}}{n+1}+C$

$\int \sin kx~dx = -\frac{1}{k}\cos kx +C$

$\int \cos kx~dx =\frac{1}{k}\sin kx +C$

**cjdyer** · June 8th 2010, 03:37 AM

Cheers for that but i really need some worked examples so i can contnue with my project

**pickslides** · June 8th 2010, 03:42 AM

Follow this for your first question,

$\int 9x^2~dx = \frac{9x^{2+1}}{2+1}+C= \frac{9x^{3}}{3}+C= 3x^3+C$

what do you get?

**cjdyer** · June 8th 2010, 03:48 AM

3x7 + c i get to here then dont know what to do?
7

**pickslides** · June 8th 2010, 03:50 AM

Originally Posted by cjdyer

3x7 + c i get to here then dont know what to do?
7

You are finished, this is correct, try the next one.

**cjdyer** · June 8th 2010, 03:55 AM

4x5 + c?
5

**pickslides** · June 8th 2010, 02:09 PM

Originally Posted by cjdyer

y = 4x4 +3

Here's another example to follow

$\int 5x^3+7~dx = \frac{5x^{3+1}}{3+1}+7x+C=\dots$

The reason for this being

$\int a~dx=ax+C$ for $a,C\in\mathbb{R}$

Originally Posted by cjdyer

y = (5-3x)2

And another example for this

Expanding first $(4-2x)^2 = (4-2x)(4-2x) = 16-16x+4x^2$

Now find $\int 16-16x+4x^2~dx$

**Turiski** · June 8th 2010, 02:24 PM

Originally Posted by pickslides

Some rules to help you.

$\int x^n~dx = \frac{x^{n+1}}{n+1}+C$

$\int \sin kx~dx = -\frac{1}{k}\cos kx +C$

$\int \cos kx~dx =\frac{1}{k}\sin kx +C$

Two more rules you'll need:

$\int e^x~dx = e^x$

Assuming u = g(x) $\int f(u)u'~dx = \int f(u)~du$

u in this example then acts like x in the above four.

Example of the last one (I know it's confusing)

$\int 5 \sin 2x ~ dx$

Here $u = 2x$ so $u' = 2$

So $\int \frac{5}{2} \sin (u)u' ~ dx = \int \frac{5}{2} \sin (u) ~ du$

$= \frac{5}{2}(-cos(u)) + C$

$= - \frac{5}{2}cos(2x) + C$

**pickslides** · June 8th 2010, 02:40 PM

For the last question

$y= \frac{e^{3x}+7}{e^x}= \frac{e^{3x}}{e^x}+ \frac{7}{e^x} = e^{2x}+7e^{-x}<br />$

**Plato** · June 8th 2010, 02:41 PM

Originally Posted by cjdyer

i would greatly appreciate if someone could work these out for me, because im struggling and need some examples on how to intergrate
bold letter are powers!

Why not learn to post in symbols? You can use LaTeX tags.
[tex]x^5+9=2[/tex] gives $x^5+9=2$ .

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