Question

For the region bounded by y=3x, the x-axis, and x=4, determine the volume when

Answer 1

The area bounded by the line y=3x from limits x=0 to x=4 will be 24.

What is integration?

Integration is defined as the adding up all the small units to find the whole unit.

It is given in the question that the line y=3x is making a region in a plane from the limits x= to x=4.

So by integrating the function we will get the area.

$\int\limits^4_0 y=\int\limits^4_0 {3x} \, dx$

$\int\limits^4_0 y=3 \int\limits^4_0 {x} \, dx$

$\int\limits^4_0 y=[\dfrac{3x^2}{2}]^4_0$

$\int\limits^4_0 y= \dfrac{(3\times (4)^2)}{2}$

$\int\limits^4_0 y= 24$

hence the region bounded by the line y=3x will have the area of 24 square units.

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