Question

Find the area bounded by the curve y=3x x axis and the ordinate x=1 x=3

Answer 1

Answer:

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Answer 2

Concept:

The area under a curve: It is the area that exists between two points on the graph and can be calculated by solving a definite integral between those two points.

Given:

y = 3 x

x - axis

The ordinate:  x = 1 and  x = 3.

Find:

We need to find the area bounded by these curves.

Solution:

As we can see in the graph, the area bounded by the curve will be:

Area = A = ∫ 3x dx   ( from 1 to 3)

Integrating the expression:

A = 3 x² / 2   ( from 1 to 3)

Solving the expression:

A = 3 / 2  [ 9 - 1 ]

A = 3 / 2 ( 8 )

A = 3 ( 4 )

A = 12 square units.

Therefore, the area bounded by the curves is 12 square units.

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