Question

TOLONG DIBANTU. PAKE CARANYA YAA. MAKASIH SEBELUMNYA.

Answer 1

Nomor 3.
a.)
int x⁻² dx
= 1/(-2+1) x^(-2+1)+C
= 1/(-1) . x⁻¹ + C
= -x⁻¹ + C
= -1/x + C

b.)
int 2x⁻³ dx
= 1/(-3+1) . 2x^(-3+1)+C
= -1/2 . 2 x⁻² + C
= -x⁻² + C
= -1/x² + C

c.)
int x^(-1/2) dx
= 1/(-1/2 +1) . x^(-1/2 + 1) + C
= 1/(1/2) . x^(1/2) + C
= 2√x + C

d.)
int x^(1/3) dx
= 1/(1/3+1) . x^(1/3+1) + C
= 1/(4/3) . x^(4/3) + C
= 3/4 x.∛x + C

e.)
int 5x^(-1/3) dx
= 5/(2/3) .x^(2/3) + C
= 15/2 . ∛x² + C

f.)
int 2/3 x^(-3/2) dx
= 2/3.1/(-1/2) . x^(-1/2) + C
= 2/3 (-2) . x^(-1/2) + C
= -4/[3√x] + C

g.)
int 100 x^(-1/4) dx
= 100. 1/(3/4) x^(3/4) + C
= 400/3 x^(3/4) + C

h.)
int a/b x^(n-1) dx
= a/b. 1/n . x^n + C
= a/(bn) . x^n + C

Nomor 4.
a.)
int f(x) dx
= 8/(3+1) x^(3+1) + 4/(1+1) x^(1+1) + C
= 2x⁴ + 2x² + C
= 2 (x⁴+x²) + C
= 2.g(x) + C

b.)
int f(x) dx
= 1/(1/2+1) x^(1/2+1) + C
= 1/(3/2) x^(3/2) + C
= 2/3 x√x + C
= 2/3 g(x) + C

c.)
int f(x) dx
= (x+2)'/(3+1) . (x+2)^(3+1) + C
= 1/4.(x+2)⁴ + C
= 1/4 g(x) + C

Nomor 5.
Terdapat pada lampiran.
Dengan int m dx
= 1/3 x^3 - x + C