The area of the region enclosed by the lines | vedclass

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

Question

(C) The lines are $y = 2x$, $y = x/2$, and $x = 2$.The intersection of $y = 2x$ and $y = x/2$ is at $(0, 0)$.The intersection of $y = 2x$ and $x = 2$

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(C) The lines are $y = 2x$, $y = x/2$, and $x = 2$.The intersection of $y = 2x$ and $y = x/2$ is at $(0, 0)$.The intersection of $y = 2x$ and $x = 2$ is at $(2, 4)$.The intersection of $y = x/2$ and $x = 2$ is at $(2, 1)$.The area $A$ is given by the integral $\int_{0}^{2} (2x - x/2) \, dx$.$A = \int_{0}^{2} (3x/2) \, dx$.$A = \frac{3}{2} \left[ \frac{x^2}{2} ight]_{0}^{2}$.$A = \frac{3}{4} [4 - 0] = 3 	ext{ sq. units}$.

The area of the region enclosed by the lines $y = 2x$, $2y = x$ and $x = 2$ (in sq. units) is...

Similar Questions

The area (in sq. units) bounded by $x^2=y$,$y=x+2$ and the $X$-axis is

The area (in square units) bounded by the line $y = x$, the $X$-axis and the lines $x = -2$ and $x = 4$ is...

The area of the region $\{(x, y) : y \le x - |x|, y \le |x \sin x|, y \ge 0\}$ is:

The area of the region bounded by the parabola $y^2 = 8x$ and its latus rectum is . . . . . . sq. units.

If a curve $y = a\sqrt{x} + bx$ passes through the point $(1, 2)$ and the area bounded by the curve,the line $x = 4$,and the $X$-axis is $8$ sq. units,then:

Vedclass Test Series

Exam Paper Generator

Online Exam Module