Solution: The area lying between the curve, $y^{2}=4 x$ and $y=2 x$, is represented by the shaded area OBAO as Points of intersection of these curves are $O(0,0)$ and $A(1,2)$. Draw AC perpendicular...
Choose the correct answer: Area lying between the curves $y^{2}=4x$ and $y=2x$ is:
Choose the correct answer: Smaller area enclosed by the circle $x^{2}+y^{2}=4$ and the line $x+y=2$ is
A. $2(\pi-2)$
B. $\pi-2$
C. $2 \pi-1$
D. $2(\pi+2)$
Solution: The smaller area enclosed by the circle, $x^{2}+y^{2}=4$, and the line, $x+y=2$, is represented by the shaded area ACBA as It is observed that, $\text { Area } A C B A=\text { Area } O A C...
Using integration find the area of the triangular region whose sides have the equations y $=2 x+1, y=3 x+1$ and $x=4$
Solution: The eqs. of the sides of the triangle are $y=2 x+1, y=3 x+1$, and $x=4$. On solving these eqs., we get the vertices of triangle as $\mathrm{A}(0,1), \mathrm{B}(4,13)$, and $\mathrm{C}$...
Using integration finds the area of the region bounded by the triangle whose vertices are $(-1,0),(1,3)$ and $(3,2)$
Solution: $\mathrm{BL}$ and $\mathrm{CM}$ are drawn perpendicular to $x$-axis. It is observed in the following figure that, Area $(\triangle \mathrm{ACB})=$ Area (ALBA) $+$ Area (BLMCB) - Area...
Find the area of the region bounded by the curves $y=x^{2}+2$, $y=x$, $x=0$ and $x=3$.
Solution: The area of the region bounded by the curves $y=x^{2}+2$, $y=x$, $x=0$ and $x=3$ is represented by the shaded area OCBAO as Therefore, Area of OCBAO = Area of ODBAO - Area of ODCO...
Find the area bounded by the curves $(x-1)^{2}+y^{2}=1$ and $x^{2}+y^{2}=1$
Solution: The area bounded by the curves $(x-1)^{2}+y^{2}=1$ and $x^{2}+y^{2}=1$ is reprsented by the shaded area as On solving the equations, $(x-1)^{2}+y^{2}=1$ and $x^{2}+y^{2}=1$, we get the...
Find the area of the circle $4x^{2}+4y^{2}=9$ which is interior to the parabola $x^{2}=4y$.
Solution: Required area is represented by the shaded area OBCDO On solving the given equation of circle, $4 x^{2}+4 y^{2}=9$, and parabola, $x^{2}=4 y$, we get $\mathrm{B}\left(\sqrt{2},...