Application of Integrals Test

Result

Application of Integrals Test - 66

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Weekly Quiz Competition

Question 1
1 / -0

Let $$f\left( x \right) =maximum\quad \left\{ { x }^{ 2 },\left( 1-x \right) ^{ 2 },2x\left( 1-x \right) \right\} $$ where $$x\epsilon \left[ 0,1 \right] $$. The area of the region bounded by the curve $$v$$ and the lines $$y=0,x=0,x=1$$

A
$$\frac { 17 }{ 27 } $$

B
$$\frac { 27 }{ 17 } $$

C
$$\frac { 17 }{ 9 } $$

D
None of these

Solution
Question 2
1 / -0

The area of the region bounded by the limits x = 0,$$x\quad =\quad \frac { \pi }{ 2 } $$ and f(x)=sinx, g(x) = cos x is:-

A
$$2(\sqrt { 2 } +1)$$

B
$$\sqrt { 3 } -1$$

C
$$2(\sqrt { 3 } -1)$$

D
$$2(\sqrt { 2 } -1)$$

Solution
Question 3
1 / -0

The area bounded by the curve $${ x }^{ 2/3 }+{ y }^{ 2/3 }={ a }^{ 2/3 },+vex-axis\& +vey-axis\quad is$$ :-

A
$$\dfrac { { \pi a }^{ 2 } }{ 32 } $$

B
$$\dfrac { 3{ \pi a }^{ 2 } }{ 32 } $$

C
$$\dfrac { 5{ \pi a }^{ 2 } }{ 32 } $$

D
$$\dfrac { 3{ \pi a }^{ 2 } }{ 16 } $$

Solution
Question 4
1 / -0

The area bounded by the curve $$y^2=4x$$ with the line x=1,x=9 is

A
$$\cfrac {436}{15}$$

B
$$\cfrac {208}{3}$$

C
$$\cfrac {236}{5}$$

D
$$\cfrac {340}{13}$$

Solution
Question 5
1 / -0

The area bounded by the curve $$y= x+\sin x$$ and its inverse function between the ordinates $$x= 0$$ and $$x= 2\pi$$ is

A
$$8 \pi$$ sq unit

B
$$4 \pi$$ sq unit

C
$$8$$ sq unit

D
None of these

Solution
Question 6
1 / -0

Area bounded by $$y|y|-x|x|=1,\ y|y|+x|x|=1$$ and $$y=|x|$$ is

A
$$\dfrac{\pi}{2}$$

B
$${\pi}$$

C
$$\dfrac{\pi}{4}$$

D
$$None\ of\ these$$

Solution
Question 7
1 / -0

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

A
$$\dfrac { 59 }{ 12 }$$

B
$$\dfrac { 3 }{ 2 }$$

C
$$\dfrac { 7 }{ 3 }$$

D
$$\dfrac { 5 }{ 2 }$$

Solution
Question 8
1 / -0

The area of the region enclosed by $$y={ x }^{ 3 }-{ 2x }^{ 2 }+2$$ and $$y=3x+2$$ is

A
$$\frac { 71 }{ 6 } $$

B
14

C
$$\frac { 39 }{ 3 } $$

D
$$\frac { 71 }{ 3 } $$

Solution
Question 9
1 / -0

The area of region $$\{ (x,y):{ x }^{ 2 }+{ y }^{ 2 }\le 1\le x+y\} $$ is:

A
$$\frac { { \pi }^{ 2 } }{ 5 } sq.$$ unit

B
$$\frac { { \pi }^{ 2 } }{ 2 } sq.$$ unit

C
$$\frac { { \pi }^{ 2 } }{ 4 } sq.$$ unit

D
$$\left( \frac { \pi }{ 4 } -\frac { 1 }{ 2 } \right) sq.$$ unit

Solution
Question 10
1 / -0

The area enclosed by $$|x - 1| + |y - 3| = 1$$ is equal to

A
4 sq. units

B
6 sq. units

C
1 sq. units

D
2 sq. units

Solution