Applications (Finding Areas and Volumes)

Q. The volume generatred by revolving the area bounded by the parabola $y^2=8x$ and the line $x=2$ about $y=$axis is

1. $\frac{128\pi }{5}$
2. $\frac{5}{128\pi }$
3. $\frac{127}{5\pi }$
4. None of above

Q. What is the area common to the circle $r=a$ and $r=2acos\theta ?$

1. $0.524a^2$
2. $0.614a^2$
3. $1.047a^2$
4. $1.228a^2$

Q. The area bounded by the parabola $2y=x^2$ and the line $x=y-4$ is equal to

1. $6$
2. $18$
3. $\infty$
4. None of the above

Q. The area between the parabola $x^2=8y$ and the straight line $y=8$ is

1. 85.33

Q.

What is the area bounded by the curve $y=\frac{1}{2}{x}^2$, the $X-axis$ and the line $x=2$ .

1. $\frac{1}{3}$

2. $\frac{2}{3}$

3. $1$

4. $\frac{4}{3}$

Q. The area enclosed between the straight line $y=x$ and the parabola $y=x^2$ in the $x-y$ plane is

1. $\frac{1}{6}$
2. $\frac{1}{4}$
3. $\frac{1}{3}$
4. $\frac{1}{2}$

Q. The area between the parabola is $y^2=2axand{x}^2=2ay$

1. $\frac{2a^2}{3}$
2. $\frac{4a^2}{3}$
3. $3a^2$
4. $\frac{8a^2}{3}$

Q. The value of the integral of the function $g(x,y)=4x^3+10y^4$ along the straight line segment from the point $(0,0)$ to the point $(1,2)$ in the $xy$ plane is

1. $33$
2. $35$
3. $40$
4. $56$

Q. Area bounded by the curve $y=x^2$ and lines $x=4$ and $y=0$ is given by,

1. $64$
2. $\frac{64}{3}$
3. $\frac{128}{3}$
4. $\frac{128}{4}$

Q. The area enclosed between the curves
$y^2=16xand{x}^2=16y$ is

1. 2048
2. 85.33
3. 2133.33
4. 1962.67

Q.

The area of the segment cut off from the parabola is

$x^2=4y$ by the line x - 2y + 4 = 0

1. 9
2. 12
3. 16
4. 24

Q. The area of the region bounded by the parabola $y=x^2+1$ and the straight line $x+y=3$ is

1. $\frac{59}{6}$
2. $\frac{9}{2}$
3. $\frac{10}{3}$
4. $\frac{7}{6}$

Q. $\text{A triangle in the xy plane is bounded by the straight lines}3x=4y,y=0\text{and}x=4\text{. The volume above the triangle and under the plane}x+y+z=8\text{is}$

1. 26