Test Details

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Application of Integrals

Test 3

Jan 01, 9:30 PM

90 minutes

Jan 01, 11:00 PM

60.0 marks

MCQ

25 questions

times Academy

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Class Details

Maths

Physics

Chemistry

Class 12th

Maths

Physics

Chemistry

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Question Text

Question 1 :
 Area bounded by the curve $\mathrm{y}=\mathrm{x}+\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{x}$ and its inverse function between the ordinates $\mathrm{x}=0$ and $\mathrm{x}=2\pi$ is

Question 2 :
 The area bounded by the curves $\mathrm{y}=$ cosx and $\mathrm{y}=$ sinx between the ordinates $\mathrm{x}=0$ and $\displaystyle \mathrm{x}=\frac{3\pi}{2}$:

Question 3 :
The area common to the parabola $y=2{ x }^{ 2 }\quad$ and $\quad y={ x }^{ 2 }+4$

Question 4 :
The area bounded by $y = xe^{|x|} $ and lines $|x| = 1, y = 0$ is

Question 5 :
The area of the region bounded by the curves $y={ xe }^{ x },y={ xe }^{ -x }$ and the line $x=1$ is

Question 6 :
The curves $y = x^{2} - 1, y = 8x - x^{2} - 9$ at

Question 7 :
The area of the region bounded by the curves $y=xe^{x}, y=xe^{-x}$ and the line $\left| x \right| =1,y=0$ is:

Question 8 :
The area bounded by $ \displaystyle y=\frac{3x^{2}}{4} $ and the line $ \displaystyle 3x-2y+12=0 $ is:

Question 9 :
The area bounded by $y = f\left( x \right),x - axis$ and the line $y = 1$, where $f\left( x \right) = 1 + \dfrac{1}{x}\int\limits_1^x {f\left( t \right)dt} $  is

Question 10 :
Find the area of the region bounded by the curves ${y}^{2}=4ax$ and ${x}^{2}=4ay$.

Question 11 :
If the line $y = \sqrt{2}x$ cuts the curve $x^2 + y^2 - 9 = 0$ at the points A, B then AB is

Question 12 :
The area of the region bounded by the curve $y=2x-x^2$ and the line $y=x$ is ________ square units.

Question 13 :
Compute the area of the figure bounded by straight lines $x = 0$, $x = 2$ and the curves $y = 2^{x}$ and $y = 2x - x^{2}$.

Question 14 :
 The area bounded by $y=x^{2}, y=[x+1],\ x\leq 1$ and the $\mathrm{y}$-axis is

Question 15 :
The area of the plane region bounded by the curve $x + 2 y ^ { 2 } = 0$ and $x + 3 y ^ { 2 } = 1$ is equal to:

Question 16 :
The area bounded by the graph $y=\left|\left[x-3\right]\right|$, the $x-$axis and the lines $x=-2$ and $x=3$ is ($\left[.\right]$ denotes the greatest Integer function):

Question 17 :
The area bounded by the curve $y={ e }^{ x }$ and the lines y = |x - 1|, x = 2 is given by :

Question 18 :
The area bounded by tangent, normal and x-axis at $\mathrm{P}(2,4)$ to the curve $y=x^{2}$

Question 19 :
 The area bounded by the line $\mathrm{x}=1$ and the curve $\sqrt{\dfrac{y}{x}}+\sqrt{\dfrac{x}{y}}=4$ is

Question 21 :
The area bounded by $y=\sec^ {-1}{x}, y= \text{cosec}^{-1}{x}$ and the line $x-1=0$ is:

Question 22 :
The area bounded by two branches of the curve $(y-x)^{2}=x^{3} \& x=1$ equals

Question 23 :
Let $A(k)$ be the are bounded by the curves $y=x^{2}-3$ and $y=kx+2$.

Question 24 :
If the area bounded by the curves $y=a{ x }^{ 2 }$ and $x=a{ y }^{ 2 }$, $(a>0)$ is $1$ sq.units, then the value of $a$ is

Question 25 :
The whole area of the curves $x=a\cos^3t, y=b\sin^3t$ is given by?

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