Application of Integrals Test

Result

Application of Integrals Test - 69

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Weekly Quiz Competition

Question 1
1 / -0

The area of the region $$x+y\le 6$$, $$x^2+y^2\le 6y$$ and $$y^2\le 8x$$ is

A
$$\cfrac{1}{72}(27\pi - 5)$$ sq.units

B
$$\cfrac{1}{12}(27\pi +2)$$ sq.units

C
$$\cfrac{1}{12}(27\pi -2)$$ sq.units

D
none of these

Solution
Question 2
1 / -0

The area of the region $$A = \{ ( x , y ) : 0 \leq y \leq x | + 1 \text { and } - 1 \leq x \leq 1 \}$$ in sq. units, is:

A
$$\frac { 4 } { 3 }$$

B
$$\frac { 2 } { 3 }$$

C
$$\frac { 1 } { 3 }$$

D
2

Solution
Question 3
1 / -0

Area of the region enclosed between the curves $$x={ y }^{ 2 }-1$$ and $$x=|y|\sqrt { 1-{ y }^{ 2 } } $$ is

A
$$1$$ sq. units

B
$$\dfrac{4}{3}$$ sq. units

C
$$\dfrac{2}{3}$$ sq. units

D
$$2$$ sq. units

Solution
Question 4
1 / -0

$$R=((x,y):|x|\le |y|\quad and\quad { x }^{ 2 }+{ y }^{ 2 }\le 1)is$$

A
$$\dfrac { 3\pi }{ 8 } s.q.units$$

B
$$\dfrac { \pi }{ 8 } s.q.units$$

C
$$\dfrac { 5\pi }{ 8 } s.q.units$$

D
$$\dfrac { \pi }{ 2 } s.q.units$$
Question 5
1 / -0

The area (in sq units) of the region $$\left\{ {\left( {x,y} \right):x \geqslant 0,x + y \leqslant 3,{x^2} \leqslant 4y\,\,and\,\,y \leqslant 1 + \sqrt x } \right\}$$ is

A
59 / 12

B
3 / 2

C
7 / 3

D
5 / 2

Solution
Question 6
1 / -0

The area of the region:
$$A = \left\{ {\left( {x,y} \right)} \right\}:0\underline < y\underline < \left| x \right| + 1\,\,{\text{and}}\,\,\left. { - 1\underline < x\underline < 1} \right\}$$ in sq. units, is

A
$$\frac{2}{3}$$

B
2

C
$$\frac{4}{3}$$

D
$$\frac{1}{3}$$

Solution
Question 7
1 / -0

Area enclosed by $$|x-1|+|y+1|=1$$.

A
2

B
4

C
1

D
8

Solution
Question 8
1 / -0

Area enclosed by the graph of the function $$y=l{ n }^{ 2 }x-1$$ lying in the $${ 4 }^{ th }$$ quadrant is

A
$$\frac { 2 }{ e } $$

B
$$\frac { 4 }{ e } $$

C
$$2(e+\frac { 1 }{ e } )$$

D
$$4(e-\frac { 1 }{ e } )$$

Solution
Question 9
1 / -0

The area of the region bounded by the curve $$x=\sin ^{-1}y$$, the x-axis and the line |x|=1 is

A
$$2-2\cos 1$$

B
$$1-\cos 1$$

C
$$1-2\cos 1$$

D
none of these
Question 10
1 / -0

The area enclosed within the curve is $$\left| x \right| + \left| y \right| = 1$$ is

A
$$\sqrt 2 $$

B
$$1$$

C
$$\sqrt 3 $$

D
$$2$$

Solution