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INTEGRAL

Jika f(x) adalah fungsi yang differensiabel maka

 dx)x('f adalah  c)x(f

A. Rumus Dasar

1.   

  c 1nx 1n

1 dx nx dengan  1n

2.      cxlndx 1 xdx x

1

3.  cxcosxdxsin 

4.   cxsinxdxcos

5.   cxtanxdx 2 sec

6.   cxcotxdx 2 csc

7.   cxsecxdxtan.xsec

8.   cxcscxdxcot.xcsc

B. Integral tentu

Jika maka   c)x(gdx)x(f

)a(g)b(g)x(gdx)x(f

b

a

b

a

 

C. Sifat-sifat integral

1.       dx)x(gdx)x(fdx)x(g)x(f

2.       dx)x(gdx)x(fdx)x(g)x(f

3.   dx)x(fkdx)x(kf

4. dx)x(fdx)x(f

a

b

b

a

 

5. dx)x(fdx)x(fdx)x(f

c

a

c

b

b

a

 

6. 0dx)x(f

a

a

 

x = a x = b

y = f(x)

y = g(x)

L =    

b

a

dx)x(g)x(f

D. Menghitung luas daerah

a b

y = f(x)

x

L= dx)x(f

b

a



a b

y = f(x)

x

L= dx)x(f

b

a

 

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E. Volume Benda Putar

a b x

y = f(x)

v =  

b

a

2

dxy a

b

y

x = f(y)

v =  

b

a

2

dyx

F Integral Parsial

duvuvdvu  

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