MCQ
$\int_{\,0}^{\,2a} {f(x)dx = } $
  • A
    $2\int_{\,0}^{\,a} {\,f(x)dx} $
  • B
    $0$
  • $\int_{\,0}^{\,a} {\,f(x)dx + \int_{\,0}^{\,a} {\,f(2a - x)dx} } $
  • D
    $\int_{\,0}^{\,a} {f(x)dx + } \int_{\,0}^{\,2a} {\,f(2a - x)dx} $

Answer

Correct option: C.
$\int_{\,0}^{\,a} {\,f(x)dx + \int_{\,0}^{\,a} {\,f(2a - x)dx} } $
c
(c) It is a fundamental property.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

Let $A =\left[\begin{array}{cc}1 & -1 \\ 2 & \alpha\end{array}\right]$ and $B =\left[\begin{array}{ll}\beta & 1 \\ 1 & 0\end{array}\right], \alpha, \beta \in R$. Let $\alpha_{1}$ be the value of $\alpha$ which satisfies $( A + B )^{2}= A ^{2}+\left[\begin{array}{ll}2 & 2 \\ 2 & 2\end{array}\right]$ and $\alpha_{2}$ be the value of $\alpha$ which satisfies $( A + B )^{2}= B ^{2}$. Then $\left|\alpha_{1}-\alpha_{2}\right|$ is equal to.
From a lot of $12$ items containing $3$ defectives, a sample of $5$ items is drawn at random. Let the random variable $\mathrm{X}$ denote the number of defective items in the sample. Let items in the sample be drawn one by one without replacement. If variance of $X$ is $\frac{m}{n}$, where $\operatorname{gcd}(m, n)=1$, then $n-m$ is equal to..........
The ${20^{th}}$ term of the series $2 \times 4 + 4 \times 6 + 6 \times 8 + .......$ will be
On the ellipse $\frac{x^{2}}{8}+\frac{y^{2}}{4}=1$ let $P$ be a point in the second quadrant such that the tangent at $\mathrm{P}$ to the ellipse is perpendicular to the line $x+2 y=0$. Let $S$ and $\mathrm{S}^{\prime}$ be the foci of the ellipse and $\mathrm{e}$ be its eccentricity. If $\mathrm{A}$ is the area of the triangle $SPS'$ then, the value of $\left(5-\mathrm{e}^{2}\right) . \mathrm{A}$ is :
A vertical line passing through the point $(h, 0)$ intersects the ellipse $\frac{x^2}{4}+\frac{y^2}{3}=1$ at the points $P$ and $Q$. Let the tangents to the ellipse at $P$ and $Q$ meet at the point $R$. If $\Delta(h)=$ area of the triangle $P Q R, \Delta_1=\max _{1 / 2 \leq h \leq 1} \Delta(h)$ and $\Delta_2=\min _{1 / 2 \leq h \leq 1} \Delta(h)$, then $\frac{8}{\sqrt{5}} \Delta_1-8 \Delta_2=$
If $\sum \limits_{i=1}^{n}\left(x_{i}-a\right)=n$ and $\sum \limits_{i=1}^{n}\left(x_{i}-a\right)^{2}=n a,(n, a>1)$ then the standard deviation of $n$ observations $x _{1}, x _{2}, \ldots, x _{ n }$ is
Suppose the vectors $x_{1}, x_{2}$ and $x_{3}$ are the solutions of the system of linear equations, $Ax = b$ when the vector $b$ on the right side is equal to $b _{1}, b _{2}$ and $b _{3}$ respectively. If $x =\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right], x _{2}=\left[\begin{array}{l}0 \\ 2 \\ 1\end{array}\right], x _{3}=\left[\begin{array}{l}0 \\ 0 \\ 1\end{array}\right], b _{1}=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right]$ $b _{2}=\left[\begin{array}{l}0 \\ 2 \\ 0\end{array}\right]$ and $b _{3}=\left[\begin{array}{l}0 \\ 0 \\ 2\end{array}\right],$ then the determinant of $A$ is equal to
Let $a=\cos 1^{\circ}$ and $b=\sin 1^{\circ}$. We say that a real number is algebraic if it is a root of a polynomial with integer coefficients. Then,
If $A = \left[ {\begin{array}{*{20}{c}}2&{ - 3}\\{ - 4}&1\end{array}} \right],$ then $adj\;\left( {3{A^2} + 12A} \right) = $ . . . .
$\int_{\,0}^{\,\infty } {\frac{{x\ln x\,dx}}{{{{(1 + {x^2})}^2}}}} $ is equal to