Pelajaran kelas baru:Integral

Coba soal-soal ini
1. $\int\frac{xdx}{\sqrt{x-1}}=...$
2. $\int\frac{x^3}{x^2+2}dx=...$

naruto wrote (View Post): › 2. $\int\frac{x^3}{x^2+2}dx=...$

Spoilers:

You have posted in this forum: Sat Jul 25, 2009 7:45 am Post subject:

@atas: jangan jawab sependek itu dong! jawab yang komplit

tambahan:
3. $\int cos^5xdx=...$
4. $\int(x^2+1)cosxdx=...$

You have posted in this forum: Sat Jul 25, 2009 7:57 am Post subject:

naruto wrote (View Post): › @atas: jangan jawab sependek itu dong! jawab yang komplit

Saya tdk bermaksud menjawab soal tsb kok naruto Smile

Saya hanya mencoba memberi hint Smile

You have posted in this forum: Sat Jul 25, 2009 11:01 am Post subject:

1. subtitusi trigono : misalkan $x = {sec}^{2}\theta$

2. subtitusi trigono : misalakan $x = \sqrt{2} {tan}^{2}\theta$

3. $\int {cos}^{5}x dx = \int {cos}^{4}x cos (x) dx = \int {(1- {sin}^{2}x)}^{2} d(sin x), mis : sin x = u$
jadi $\int {(1- {u}^{2})}^{2} d(u)$ , selesai deh..

4. jabarin trus yg ad faktor ${x}^{2}$ ny pake integral parsial..

sorry klo salah..

You have posted in this forum: Sat Aug 01, 2009 11:42 pm Post subject:

Ada lagi
5. $\int sin4xcos2xdx=...$
6. $\int sin(x-\frac12\pi)sin(x+\frac13\pi)dx=...$
7. $\int x^2lnxdx=...$

$\text{HINT}$
5. Kita kan punya rumus $2\sin a \cos b = \sin(a+b)+\sin(a-b)$ , pake itu aja.. Truz diintegralin tiap suku. Selesai.

6. Kita juga punya $-2 \sin a \sin b = \cos(a+b) - \cos(a-b)$ .

7. Integration by parts $\int u dv = uv - \int v du$ . Sepertinya butuh dua kali pemarsialan.
$u = x^2$ , $dv= \ln x dx$

You have posted in this forum: Tue Aug 11, 2009 4:04 am Post subject:

No 2 gampang tgl dibagi aja

$\int\frac{x^3}{x^2+2} dx$
$\int x - \frac{2x}{x^2+2} dx$
$\frac{x^2}{2} - \int \frac{2x}{x^2+2} \frac{d(x^2+2)}{2x}$
$\frac{x^2}{2} - ln(x^2+2)+c$

BERES!!!

You have posted in this forum: Tue Aug 11, 2009 8:39 am Post subject:

Kalo yang ini gimana:
$\gammacorrection{1.2}\int sin^2x.e^{2x}dx=...$
NB: Hint ato solusi buat yang ini tolong di spoiler dulu

You have posted in this forum: Tue Aug 11, 2009 2:08 pm Post subject:

Hint untuk solusi 2

Spoilers:

You have posted in this forum: Thu Aug 13, 2009 10:10 am Post subject:

@silvergrasshopper : Nomor 7 milih u sama v nya kebalik, kalo mau lebih gampang sih..

@Adri : De Moivre ga diajarin di skul lho, jangan pake lah itu identitas Big Grin

Lebih menarik solusi 2 Big Grin