Question

Giúp mình với ạ

Answer 1

GiuG mình câu 1😒 với câu 3a

Answer 2

Ta có : \(\int f\left(x\right)dx=\int sin^3x.cosx.dx=\int sin^3x.d\left(sinx\right)=\dfrac{sin^4x}{4}+C\)

Answer 3

3.

\(x\left(2-f'\left(x\right)\right)=f\left(x\right)+1\Leftrightarrow x.f'\left(x\right)+f\left(x\right)=2x-1\)

\(\Leftrightarrow\left[x.f\left(x\right)\right]'=2x-1\)

Lấy nguyên hàm 2 vế:

\(x.f\left(x\right)=\int\left(2x-1\right)dx=x^2-x+C\)

Thay \(x=2\Rightarrow6=2+C\Rightarrow C=4\)

\(\Rightarrow f\left(x\right)=\dfrac{x^2-x+4}{x}\Rightarrow f\left(4\right)=4\)