Aku n MATEMATIKA cah SMA Nda: SOAL n PEMBAHASAN INTEGRAL

N0-1
$\int \frac{x^{2}+4x-1}{x^{2}-1}.dx=....$

JAWAB :
$\int \frac{x^{2}+4x-1}{x^{2}-1}.dx=\int \frac{x^{2}-1+4x}{x^{2}-1}.dx=\int \left (\frac{x^{2}-1}{x^{2}-1}+\frac{4x}{x^{2}-1} \right ).dx$

$=\int \left (1+\frac{4x}{x^{2}-1} \right ).dx=x+\int \frac{4x}{x^{2}-1} .dx$

$=x+\int \frac{4x}{x^{2}-1} .\frac{d(x^{2}-1)}{2x}=x+2.ln\left | x^{2}-1 \right |+c$

${\color{Red} INGAT\,\, !!!}\: \: \: \int \frac{d\, \blacksquare }{\blacksquare } =ln\left | \blacksquare \right |+c$

NO-2
$Hasil\: \int \frac{x+3}{\sqrt{x-3}}.dx=....$

JAWAB :
$misal\: jika\: \: y=x-3 \: maka \: dy=dx$
$\int (y+6).y^{-\frac{1}{2}}.dy=\int (y^{\frac{1}{2}}+6y^{-\frac{1}{2}}).dy=\frac{2}{3}y^{\frac{3}{2}}+6.\frac{2}{1}y^{\frac{1}{2}}+c$
$=\sqrt{x-3}.(\frac{2}{3}.x+10)+c$

NO-3
$\int sin^{3}x.cos^{^{2}}x.dx=....$

JAWAB :
$\int {\color{Red} sin^{2}x}.cos^{^{2}}x.{\color{Blue} sin\, x}.dx=\int {\color{Red} \left (1-cos^{2}x \right )}.cos^{^{2}}x.{\color{Blue} sin\, x}.\frac{d\left (cos\, x \right )}{sin\, x}$
$\int \left (cos^{4}x-cos^{2}x \right ){d\left (cos\, x \right )}=\frac{cos^{5}x}{5}-\frac{cos^{3}x}{3}+C$

Aku n MATEMATIKA cah SMA Nda

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Kamis, Juli 19, 2012

SOAL n PEMBAHASAN INTEGRAL_2

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