If _0^ 2a f(x) ,dx = 2 _0^a f(x) ,dx, then - Vidyadip

MCQ

If $\int_0^{2a} {f(x)\,dx = 2\int_0^a {f(x)\,dx,} } $ then

A
$f(2a - x) = - f(x)$
✓
$f(2a - x) = f(x)$
C
$f(a - x) = - f(x)$
D
$f(a - x) = f(x)$

✓

Answer

Correct option: B.

$f(2a - x) = f(x)$

b
(b) 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

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

A factory is operating in two shifts, day and night, with $70$ and $30$ workers respectively . If per day mean wage of the day shift workers is $Rs. 54$ and per day mean wage of all the workers is $Rs. 60,$ then per day mean wage of the night shift workers(in $Rs. $ )is

${x^x}$ has a stationary point at

If a right circularcone having maximum volume, is inscribed in a sphere of radius $3\, cm$, then the curved surface area (in $cm^2$) of this cone is

The elimination of the arbitrary constants $A, B$ and $C$ from $y = A + Bx + C{e^{ - x}}$leads to the differential equation

$\int_{}^{} {\sqrt {1 + \sin x} \;dx = } $

If the area bounded by $y = ax^2$ and $x = ay^2, a > 0$, is $1$ then $a =$

$2{x^3} - 6x + 5$ is an increasing function if

If $A = \left[ {\begin{array}{*{20}{c}}1&{\tan \theta /2}\\{ - \tan \theta /2}&1\end{array}} \right]$ and $AB = I$, then $B = $

If the area of the region

$\left\{(\mathrm{x}, \mathrm{y}): \frac{\mathrm{a}}{\mathrm{x}^2} \leq \mathrm{y} \leq \frac{1}{\mathrm{x}}, 1 \leq \mathrm{x} \leq 2,0<\mathrm{a}<1\right\}$ is

$\left(\log _e 2\right)-\frac{1}{7}$ then the value of $7 a-3$ is equal to:

Let $\left(\frac{n}{k}\right)=\frac{n !}{k !(n-k) !}$. Then the sum $\frac{1}{2^{10}} \sum \limits_{ k =0}^{10}\left(\frac{10}{ k }\right) k ^2$, lies in the interval