Question

Evaluate: $\int 3x-5dx$

• A. $\frac{3x^2}{2}-5x+C$
• B. $\frac{3x^2}{2}-7x+C$
• C. $\frac{3x^2}{2}-4x+C$
• D. $\frac{3x^2}{2}-6x+C$

Answer 1

The correct option is A $\frac{3x^2}{2}-5x+C$

We know that,

$\int (P+Q)dx=\int Pdx+\int Qdx$

$\int kPdx=k\int Pdx$ {where $k$ is a constant}

Hence ,

$\int (3x-5)dx=3\int xdx-5\int dx$

$\Rightarrow \int xdx=\frac{x^2}{2}+C_1\&\int dx=x+C_2\because \int x^{n}dx=\frac{x^{n+1}}{n+1}+C\therefore \int (3x-5)dx=3\frac{x^2}{2}-5x+C$

{$C$ is equal to $C_1+C_2$}