Matematika Tentukan Hasil integral Dari :a. Integral (4-x)³ dxb. Integral 4/(2x+9)² dxc. integral 2/akar 2x-1​

mathildemarquardtulv – March 04, 2023

Tentukan Hasil integral Dari :
a. Integral (4-x)³ dx
b. Integral 4/(2x+9)² dx
c. integral 2/akar 2x-1​

Jawab:

a.

[tex]\int{(4-x)^{3} } \, dx[/tex]

[tex]=\frac{1}{3+1} (4-x)^{3+1}\div (-1) +c[/tex]

[tex]=-\frac{1}{4} (4-x)^{4}+c[/tex]

b.

[tex]\int {\frac{4}{(2x+9)^{2}} } \, dx[/tex]

[tex]=\int 4(2x+9)^{-2} \, dx[/tex]

[tex]=4\int (2x+9)^{-2} \, dx[/tex]

[tex]=4[\frac{1}{-2+1} (2x+9)^{-2+1}\div (2)]+c[/tex]

[tex]=4(-\frac{1}{2} (2x+9)^{-1})+c[/tex]

[tex]=-2(2x+9)^{-1}+c[/tex]

[tex]atau = -\frac{2}{2x+9}+c[/tex]

c.

[tex]\int {\frac{2}{\sqrt{2x-1} } \, dx[/tex]

[tex]=\int {2}(2x-1)^{-\frac{1}{2} } \, dx[/tex]

[tex]=2\int (2x-1)^{-\frac{1}{2} } \, dx[/tex]

[tex]=2[\frac{1}{-\frac{1}{2}+1} (2x-1)^{-\frac{1}{2}+1 } \div(2)]+c[/tex]

[tex]=2[(2x-1)^{\frac{1}{2}}]+c[/tex]

[tex]=2(2x-1)^{\frac{1}{2}}+c[/tex]

[tex]atau = 2\sqrt{2x-1}+c[/tex]

[answer.2.content]