Question-1:Find the area of the region bounded lying in the first quadrant and bounded by thecurves x =4y2 , y-axis and the lines y = 1, y = 4Question-2:Find the area of the region enclosed by the parabola y = x² , the line y – x – 2 andthe x-axis

Answered: Question-1: Find the area of the region…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.2: Graphs Of Equations

Problem 43E

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Step 1

Given

The equation of curves is $x = 4 y^{2}$ , y axis and the lines y=1 and y=4 .

Area formula :-

$A = \int_{a}^{b} |f (y) - g (y)| d y$

Step 2

To find area of region bounded by the curve by using formula

here a =1 , b=4 , $f (y) = 4 y^{2}$ and $g (y) = 0$

$\begin{array}{rcl} A & = & \int_{1}^{4} |4 y^{2} - 0| d y \\ = & \int_{1}^{4} 4 y^{2} d y \\ = & {[\frac{4 y^{3}}{3}]}_{1}^{4} \\ = & [\frac{4 {(4)}^{3}}{3} - \frac{4 {(1)}^{3}}{3}] \\ = & [\frac{256}{3} - \frac{4}{3}] \\ = & \frac{252}{3} \\ A & = & 84 \end{array}$

Therefore , The area of region bounded by the curve is A=84 .

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