Thread: proof an integral

show in the notation of the figure that the volume of the gasoline that fills the tank to depth d is

V= 2L integral {-r , -r+d} sqrt (r^2 - y^2)dy


how can i show that ?

Let R=radius of tank and d=depth of gas.

The circle that makes up the ends of the tank can be represented by

$\displaystyle x=\pm\sqrt{R^{2}-y^{2}}$

Integrate this over the depth of the gas.

$\displaystyle \int_{-R}^{d-R}\sqrt{R^{2}-y^{2}}dy$

Multiply by L for the length of the tank and multiply by 2 to include the whole circle and not just the upper portion.

$\displaystyle 2L\int_{-R}^{d-R}\sqrt{R^{2}-y^{2}}dy$

which method should i use to evaluate the above integral ??

thnx

Originally Posted by alex83

which method should i use to evaluate the above integral ??

thnx

Maths is not a spectator sport. Review the methods you have been taught. What have you tried? Where do you get stuck?