The area of the region bounded by the curve y | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) To find the area bounded by the curve $y^2=9x$ and the line $y=3x$,we first find the points of intersection.Substituting $y=3x$ into $y^2=9x$,we g

Vedclass · Accepted Answer

$\frac{1}{2}$ sq.units

Vedclass · Answer

(C) To find the area bounded by the curve $y^2=9x$ and the line $y=3x$,we first find the points of intersection.Substituting $y=3x$ into $y^2=9x$,we get $(3x)^2=9x$,which implies $9x^2=9x$,so $x^2-x=0$,giving $x(x-1)=0$. Thus,$x=0$ and $x=1$.For $x=0$,$y=0$. For $x=1$,$y=3$.The area is given by the integral of the upper curve minus the lower curve from $x=0$ to $x=1$.$	ext{Area} = \int_0^1 (\sqrt{9x} - 3x) dx$$= \int_0^1 (3\sqrt{x} - 3x) dx$$= 3 \left[ \frac{2}{3}x^{3/2} - \frac{x^2}{2} ight]_0^1$$= 3 \left( \frac{2}{3}(1)^{3/2} - \frac{(1)^2}{2} ight) - 0$$= 3 \left( \frac{2}{3} - \frac{1}{2} ight)$$= 3 \left( \frac{4-3}{6} ight) = 3 	imes \frac{1}{6} = \frac{1}{2} 	ext{ sq.units}$.

The area of the region bounded by the curve $y^2=9x$ and the line $y=3x$ is

Similar Questions

The area (in square units) of the region bounded by the curve $y = |\sin 2x|$ and the $X$-axis in the interval $[0, 2\pi]$ is:

Area of the region bounded by the curve $y=e^x$ and lines $x=0$ and $y=e$ is

The area bounded by the curve $y = x |\sin(\frac{x}{2})|$ and the $X$-axis between the lines $x = 0$ and $x = 4\pi$ (in square units) is: (in $\pi$)

The area bounded between the curves $y=ax^2$ and $x=ay^2$ $(a > 0)$ is $1$ sq. unit. Then the value of $a$ is:

The part of the straight line $y = x + 1$ between $x = 2$ and $x = 3$ is revolved about the $x$-axis. The curved surface area of the solid thus generated is

Vedclass Test Series

Exam Paper Generator

Online Exam Module