Application of Integrals Test

Result

Application of Integrals Test - 72

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Weekly Quiz Competition

Question 1
1 / -0

Area bounded by curve $$y = (x - 1)(x - 2)(x - 3)$$ and x-axis between lines $$x = 0, x = 3$$

A
$$5/2$$

B
$$11/4$$

C
$$1$$

D
$$3$$
Question 2
1 / -0

The area of the figure bounded by $$y=sinx, \ y=cosx$$ is the first quadrant is

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

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

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

D
None of these

Solution
Question 3
1 / -0

The area bounded by the curve $$ y =x^4 -2x^3 + x^2 + 3 $$ the axis of abscissas and two oridnates corrsponding to the point of minimum of function y(x) is

A
10/3

B
27/10

C
21/10

D
None of these

Solution
Question 4
1 / -0

The area of the region bounded by $$y^2=2x +1$$ and $$x-y-1=0$$ is

A
$$\dfrac{2}{3}$$

B
$$\dfrac{4}{3}$$

C
$$\dfrac{8}{3}$$

D
$$\dfrac{16}{3}$$

Solution
Question 5
1 / -0

The area of the region enclosed by the curve $$ \mid y \mid =-(1- \mid x \mid)^2 +5 $$, is

A
$$ \dfrac{8}{3} (7 + 5 \sqrt{5}) $$ sq units

B
$$ \dfrac{2}{3} (7 + 5 \sqrt{5}) $$ sq units

C
$$ \dfrac{2}{3} (5 \sqrt{5}-7) $$ sq units

D
None of these

Solution
Question 6
1 / -0

If the area bounded by the curve $$ y=x^2 +1, y=x $$ and the pair of lines $$ x^2 + y^2 + 2xy - 4x -4y +3 =0 $$ is $$K$$ units, then the area of the region bounded by the curve $$y=x^2 +1, \ y= \sqrt{x-1}$$ and the pair of lines $$ (x+y-1)(x+y-3)=0 ,$$ is

A
$$K$$

B
$$2K$$

C
$$ \dfrac{K}{2} $$

D
None of these

Solution
Question 7
1 / -0

The area bounded by the curve $$y= \dfrac{3}{\mid x \mid}$$ and $$y+ \mid 2-x \mid =2$$ is

A
$$ \dfrac{4-log27}{3} $$

B
$$ 2-log3 $$

C
$$ 2+log3 $$

D
None of these

Solution
Question 8
1 / -0

The area bounded by the curves $$y=x^2 +2$$ and $$y=2 \mid x \mid -cosx +x$$ is

A
$$ \dfrac{2}{3} $$

B
$$ \dfrac{8}{3} $$

C
$$ \dfrac{4}{3} $$

D
$$ \dfrac{1}{3} $$

Solution
Question 9
1 / -0

The areas of the figure into which the curve $$y^2=6x$$ divides the circle $$x^2 + y^2 = 16$$ are in the ratio

A
$$ \dfrac{2}{3} $$

B
$$ \dfrac{4 \pi - \sqrt{3}}{8 \pi + \sqrt{3}} $$

C
$$ \dfrac{4 \pi + \sqrt{3}}{8 \pi - \sqrt{3}} $$

D
None of these
Question 10
1 / -0

The area bounded by the curve $$f(x) = \mid \mid tanx + cotx \mid - \mid tanx - cotx \mid \mid$$ between the lines $$x=0, \ x= \dfrac{\pi}{2}$$ and the $$X-$$axis is

A
$$ log4 $$

B
$$ log \sqrt{2] $$

C
$$ 2log2$$

D
$$ \sqrt{2} log2$$