Question:
If
\[
\int_0^a f(2a - x) \, dx = m \quad \text{and} \quad \int_0^a f(x) \, dx = n,
\]
then
\[
\int_0^{2a} f(x) \, dx
\]
is equal to:
If
\[ \int_0^a f(2a - x) \, dx = m \quad \text{and} \quad \int_0^a f(x) \, dx = n, \]
then
\[ \int_0^{2a} f(x) \, dx \]
is equal to:
\[ \int_0^a f(2a - x) \, dx = m \quad \text{and} \quad \int_0^a f(x) \, dx = n, \]
then
\[ \int_0^{2a} f(x) \, dx \]
is equal to:
Show Hint
Use substitution x→ a+b-x in definite integrals.
Updated On: Mar 23, 2026
- \(2m+n\)
- \(m+2n\)
- \(m-n\)
- m+n
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1:
\[ \int_0^{2a} f(x) \, dx = \int_0^a f(x) \, dx + \int_a^{2a} f(x) \, dx \]
Step 2: Let \(x = 2a - t\) in the second integral:
\[ \int_a^{2a} f(x) \, dx = \int_0^a f(2a - t) \, dt = m \]
Step 3:
\[ \int_0^{2a} f(x) \, dx = n + m \]
\[ \int_0^{2a} f(x) \, dx = \int_0^a f(x) \, dx + \int_a^{2a} f(x) \, dx \]
Step 2: Let \(x = 2a - t\) in the second integral:
\[ \int_a^{2a} f(x) \, dx = \int_0^a f(2a - t) \, dt = m \]
Step 3:
\[ \int_0^{2a} f(x) \, dx = n + m \]
Was this answer helpful?
0
0
Top BITSAT Mathematics Questions
- The solution of $\sin^{-1}\,x-\sin^{-1}\,2x=\pm\frac{\pi}{3}$ is
- If one root of the quadratic equation $a x^{2}+b x+c=0$ is equal to $n^{\text {th }}$ power of the other root, then the value of: $a^{\frac{n}{n-1}} C^{\frac{1}{n-1}}+c^{\frac{n}{n-1}} a^{\frac{1}{n-1}}$ is equal to
- $(x -1) (x^2 - 5x + 7) < (x -,1),$ then $x$ belongs to
- An ellipse has $OB$ as semi-minor axis, $F$ and $F$ are its foci and the $\angle FBF$, is a right angle. Then, the eccentricity of the ellipse is
- $2^{1/4}. 2^{2/8}. 2^{3/16}. 2^{4/32}......\infty$ is equal to-
View More Questions
Top BITSAT Definite Integral Questions
- If $\int \frac{\cos x-1}{\sin x+1} e^{x} d x$ is equal to:
- If $\frac{ d }{ dx }(\phi( x ))= f ( x )$, then $\int\limits_{1}^{2} f ( x )$ is equal to:
- If Im=₀¹ ( x)ᵐ dx, where mN, then I₁₀+10I₉ is equal to
- Find the value of ₀⁽⁴π⁾/⁽³⁾|sin x|dx.
- Let I₁=₀²1√(1+x²)dx and I₂=₀²(1)/(x)dx, then:
View More Questions
Top BITSAT Questions
- Two point charges $-q$ and $+ q$ are located at point's $(0, 0, - a)$ and, $(0, 0, a)$ respectively. The electric potential at a point $(0, 9, z)$, where $z > a$ is
- Which of the following must be known in order to determine the power output of an automobile?
- A large drop of oil (density $0.8 \,g / cm ^{3}$ and viscosity $\eta_{0}$ ) floats up through a column of another liquid (density $1.2\, g / cm ^{3}$ and viscosity $\eta_{L}$ ). Assuming that the two liquids do not mix, the velocity with which the oil drop rises will depend on :
- A body is projected vertically upwards at time $ t = 0$ and it is seen at a height $H$ at time $t_1$ and $t_2$ second during its flight. The maximum height attained is ($g$ is acceleration due to gravity)
- At what point of a projectile motion, acceleration and velocity are perpendicular to each other ?
View More Questions