TUGAS MANDIRI I - KALKULUS II KAMPUS MILENIAL ITBI

 NAMA         : FAZASOKHI  GIAWA

KELAS         : MALAM

JURUSAN    : TEKNIK INFORMATIKA

1.    ∫dt1+t√

       Jawab:

Misalkan :

u=1+t−−−−√

u2=1+t=2udu=dt

t=u2−1

Penyelesaian :

=∫dt1+t√

=∫t1+t√dt

=∫u2−1u2udu

=∫u2−2du

=−2∫u2du

=−213u3+C

=−23u3+C

=−23(1+3−−−−√)3+C

=−23(1+t)32+C

2.    ∫x(x2+1)4dx 

       Jawab:

Misalkan :

u=x2+1

du=2xdx→du2x=dx

Penyelesaian :

=∫x(x2+1)4dx

=∫x(u)4du2x

=∫12u4du

=12.15u5+C

=110(x2+1)5+C

3.    ∫2t3−4t−−−−−√

       Jawab:

Misalkan :

u=3−4t−−−−−√

u2=3−4t→2udu=−4dt

dt=2udu−4→−4t=u2−3→t=u2+1

Penyelesaian :

∫2t3−4t−−−−−√

=2∫(u2+1)(u)(−2u4du)

=2∫(u3+u)(−2u4du)

=2(−24)∫(u3+u)udu

=−1∫(u4+u2)du

=−1(15u5+13u3)+C

=−15(3−4t−−−−−√)5−13(3−4t−−−−−√)3+C

=−15(3−4t)52−13(3−4t)32+C