Find area of region
Question: Find area of region $\left\{(\mathrm{x}, \mathrm{y}): \mathrm{x}^{2} \leq \mathrm{y} \leq \mathrm{x}\right\}$ Solution:...
Read More →Using integration, find the area of the triangle, the equations of whose sides are
Question: Using integration, find the area of the triangle, the equations of whose sides are $y=2 x+1, y=3 x+1$ and $x=4$. Solution:...
Read More →Compare the areas under the curves
Question: Compare the areas under the curves $y=\cos ^{2} x$ and $y=\sin ^{2} x$ between $x=0$ and $x=\pi$. Solution:...
Read More →Find the area of bounded by the curve
Question: Find the area of bounded by the curve $y=\cos x$, the $x$-axis and the ordinates $x=0$ and $x=2 \pi$. Solution: ....
Read More →Find the area between the curve
Question: Find the area between the curve $y=\frac{x}{\pi}+2 \sin ^{2} x$, the axis and the ordinates $x=0$ and $x=\pi$. Solution: Given...
Read More →Find by integration the area bounded
Question: Find by integration the area bounded by the curve $y^{2}=4 a x$ and the lines $y=2 a$ and $x=0$. Solution:...
Read More →Draw a rough sketch and find the area of the region bounded
Question: Draw a rough sketch and find the area of the region bounded by the parabolas $y^{2}=4 x$ and $x^{2}=4 y$, using the method of integration. Solution:...
Read More →Draw a rough sketch of the region
Question: Draw a rough sketch of the region $\left\{(x, y): y^{2} \leq 3 x, 3 x^{2}+3 y^{2} \leq 16\right\}$ and find the area enclosed by the region, using the method of integration. Solution:...
Read More →Sketch the region common to the circlex
Question: Sketch the region common to the circlex ${ }^{2}+y^{2}=25$ and the parabola $y^{2}=8 x .$ Also, find the area of the region, using integration. Solution:...
Read More →Sketch the region common to the circle
Question: Sketch the region common to the circle $x^{2}+y^{2}=16$ and the parabola $x^{2}=6 y$. Also, find the area of the region, using integration. Solution:...
Read More →Find the area of the region enclosed between the circles
Question: Find the area of the region enclosed between the circles $x^{2}+y^{2}=1$ and $(x-1)^{2}+y^{2}=1$ Solution:...
Read More →Sketch the region lying in the first quadrant and bounded
Question: Sketch the region lying in the first quadrant and bounded by $y=9 x^{2}, x=0, y=1$ and $y=4$. Find the area of the region, using integration. Solution:...
Read More →Sketch the region lying in the first quadrant and bounded
Question: Sketch the region lying in the first quadrant and bounded by $y=4 x^{2}, x=0, y=2$ and $y=4$. Find the area of the region using integration. Solution:...
Read More →Using integration, find the area of region bounded
Question: Using integration, find the area of region bounded by the line $y-1=x$, the $x$-axis, and the ordinates $x=-2$ and $x=3$. Solution:...
Read More →Using integration, find the area of the region bounded between
Question: Using integration, find the area of the region bounded between the line $x=2$ and the parabola $y^{2}=8 x$. Solution:...
Read More →Using integration, find the area of
Question: Using integration, find the area of $\triangle \mathrm{ABC}$, the equation of whose sides $A B, B C$ and $A C$ are given by $Y=4 x+5, x+y=5$ and $4 y=x+5$ respectively. Solution:...
Read More →Using integration, find the area of the region bounded
Question: Using integration, find the area of the region bounded by the triangle whose vertices are $A(-1,2), B(1,6)$ and C $(3,4)$ Solution:...
Read More →Find the area bounded by the curve
Question: Find the area bounded by the curve $y=\left(4-x^{2}\right)$, the $y$-axis and the lines $y=0, y=3$. Solution:...
Read More →Using integration, find the area of the region bounded
Question: Using integration, find the area of the region bounded by the lines $y=1|x+1|, x=-2, x=3$ and $y=0$. Solution:...
Read More →Evaluate the area bounded by the ellipse
Question: Evaluate the area bounded by the ellipse $\frac{x^{2}}{4}+\frac{y^{2}}{9}=1$ above the $x$-axis. Solution:...
Read More →Find the area of the region bounded
Question: Find the area of the region bounded by the curve $y^{2}=4 x$ and the lines $x=3$. Solution:...
Read More →Using integration, find the area of the region bounded
Question: Using integration, find the area of the region bounded by the lines $2 y=5 x+7$, the $x$-axis and the lines $2 y=5 x+7$, the $x$-axis, and the lines $x=2$ and $x=8$. Solution: The Area of the required region $=96$ sq. units....
Read More →Determine the area under the curve
Question: Determine the area under the curve $y=\sqrt{a^{2}-x^{2}}$, included between the lines $x=0$ and $x=4$. Solution:...
Read More →Determine the area enclosed by curve
Question: Determine the area enclosed by curve $y=x^{3}$, and the lines $y=0, x=2$ and $x=4$. Solution:...
Read More →Find the area under the curve
Question: Find the area under the curve $y=\sqrt{6 x+4}$ (above the $x$-axis) from $x=0$ to $x=2$ Solution:...
Read More →