Question

The value of the integral of the function $g(x,y)=4x^3+10y^4$ along the straight line segment from the point $(0,0)$ to the point $(1,2)$ in the $xy$ plane is

• A. $33$
• B. $35$
• C. $40$
• D. $56$

Answer 1

The correct option is A $33$

Equation of straight line from
$(0,0)$ to $(1,2)$ is $y=2\left(x\right)$

So, $I=\int g(x,y)dx$
$I={\int }_0^1(4x^3+10y^4)dx$
$I={\int }_0^1[4x^3+10\times 16(x{)}^4]dx$
$=33$