Contoh praktikum kalkulus

NAMA : ALBERTUS GARUT
NIM : 2014220020

UAS PRAKTIKUM KALKULUS
>> x=sym(‘x’)
x =
x
>> f=@(x)(6*x^4+7*x^2+9)
f =@(x)(6*x^4+7*x^2+9)
>> diff(f(x))
ans =24*x^3 + 14*x
>> diff(f(x),3)
ans =144*x

1. Menentukan turunan fungsi terhadap x
>> x=sym(‘x’)
x =
x
>> f=@(x)(x^3+6*x^2-2*x+81)
f =@(x)(x^3+6*x^2-2*x+81)
>> diff(f(x),x)
ans =3*x^2 + 12*x – 2
Mencari akar-akar dari turunan dengan menggunakan solve
>> solve(3*x^2 + 12*x – 2)
ans =– 42^(1/2)/3 – 2
42^(1/2)/3 – 2

1. Mencari turunan fungsi jika terdapat lebih dari satu variabel
>> syms x y z
>> h=@(x,y,z)(sqrt(2*y^2-4*x*y)/(2*x*y*z)
>> h=@(x,y,z)(sqrt(2*y^2-4*x*y)/(2*x*y*z))
h =@(x,y,z)(sqrt(2*y^2-4*x*y)/(2*x*y*z))
>> diff(h(x,y,z),x)
ans =– 2^(1/2)/(2*x*z*(y^2 – 2*x*y)^(1/2)) – (2^(1/2)*(y^2 – 2*x*y)^(1/2))/(2*x^2*y*z)

1. Mencari turunan fungsi jika terdapat exp
>> syms x y z
>> g=@(x,y)(12*x^2*y^3+3*y^(2*x)-exp(y))
g =@(x,y)(12*x^2*y^3+3*y^(2*x)-exp(y))
>> diff(g(x,y))
ans =24*x*y^3 + 6*y^(2*x)*log(y)

2. Integral

1. Mencari integral pada suatu fungsi
>> x=sym(‘x’)
x =
x
>> f=@(x)(6*x^4+7*x^2+9)
f =@(x)(6*x^4+7*x^2+9)
>>
>> int(f(x))
ans =(x*(18*x^4 + 35*x^2 + 135))/15
1. Mencari integral kedua
>> x=sym(‘x’)
x =
x
>> f=@(x)(x+3)
f =@(x)(x+3)
>> int(f(x))
ans =(x + 3)^2/2
>> int((x + 3)^2/2)
ans =(x + 3)^3/6
>> int(int(f(x)))
ans =(x + 3)^3/6

1. Integral trigonometri
>> x=sym(‘x’)
x =x
>> f=@(x)(sec(x))^2
f =@(x)(sec(x))^2
>> int(f(x))
ans =tan(x)

1. Integral yang memiliki batas tertentu

>> x=sym(‘x’)
x =x
>> f=@(x)(2*x^2+5*x)

f =@(x)(2*x^2+5*x)

>> int(f(x),0,3)
ans = 81/2

CentralTegho

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