Question

The area bounded by the curve $y=-4x+3$ and $y=0$ between $x=2$ and $x=4$ is

• A. $26$
• B. $-20$
• C. $18$
• D. $-18$

Answer 1

The correct option is D $-18$

Area bounded by the curve is given by $A={\int }_{x_1}^{x_2}ydx$
$\Rightarrow {\int }_2^4(-4x+3)dx$
$\Rightarrow {[-2x^2+3x]}_2^4$
$\Rightarrow (-2(4{)}^2+3\times 4\left)\right)-(-2(2^2)+3\times 2)$
$\Rightarrow -32+12+8-6=-18$