Question

The area enclosed by the curve y= 4x and x=3 and x=5 is

Answer 1

The area required is 32 units square.

Given

• curve y= 4x
• x=3 and
• x=5

To find

• area enclosed by the curve

Solution

we are provided with the equation of a carbon that is Y = 4x and 2 points on the x axis that is 3 and 5 and asked to find the area enclosed between the curve and the x-axis.

the answer of this type of area estimating questions could be found out by simply substituteting the values in the standard equation.

since the curve is continuous and is differentiable on real line as it is a polynomial function we could simply in the integrate within the given limits of x axis to get the required area.

kindly refer the given attachment for the calculation part of the given question.

from the calculations, we get that the area required is 32 units square

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Answer 2

The area enclosed by the curve y= 4x and x=3 and x=5 is 32 sq-units.

Step-by-step explanation:

Given:

• A curve $y = 4x$
• Two lines $x = 3 \: and \: x = 5$

To find:

• Find the area enclosed by the curve y= 4x and x=3 and x=5.

Solution:

Concept to be used:

Area enclosed by the curve f(x) and the lines x=a and x=b is calculated as follows:

$\bf A= \int_{a}^b f(x)\:dx$

Step 1:

Write the terms used in the formula.

Here,

$f(x) = 4x$

$x = 3$

and

$x = 5$

Step 2:

Find area enclosed by curve and lines.

$A = \int_{3}^5 \: 4x \: dx$

or

$= 4 \int_{3}^5 \: x\: dx$

or

$= 4\left( \frac{ {x}^{2} }{2} \right)_{3}^5$

or

$= 4\left( \frac{25}{2} - \frac{9}{2}\right)_{3}^5$

or

$= 4\left( \frac{25 - 9}{2}\right )$

or

$= 4 \times 8$

or

$A= 32 \: sq \: units$

Thus,

The area enclosed by the curve y= 4x and x=3 and x=5 is 32 sq-units.

Learn some related questions :

1) find first quadrant area bounded by the curves using integration :

y = arctanx, y=π/4 and x=0.

https://brainly.in/question/19311774

2)find the area enclosed by the curve y=x with x-axis and x=1 using determinants

https://brainly.in/question/22949093

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