Question:medium

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:

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

The Correct Option is D

Solution and Explanation

Was this answer helpful?

0

Top Questions on Definite Integral

If \( f(x) = \int_0^x t(\sin x - \sin t)dt \) then :
- BITSAT - 2026
- Mathematics
- Definite Integral
View Solution
The value of \( \displaystyle \int_{0}^{\pi/2} \frac{\sin x}{\sin x + \cos x} \, dx \) is:
- MHT CET - 2026
- Mathematics
- Definite Integral
View Solution
Evaluate the definite integral: \( \displaystyle \int_{3}^{5} |x-4|\,dx \).
- MHT CET - 2026
- Mathematics
- Definite Integral
View Solution
Evaluate the integral \( \displaystyle \int_{0}^{\pi/2} \frac{\sin^n x}{\sin^n x + \cos^n x} \, dx \).
- MHT CET - 2026
- Mathematics
- Definite Integral
View Solution
Want to practice more? Try solving extra ecology questions todayView All Questions

Questions Asked in BITSAT exam

The locus of the mid-point of a chord of the circle \( x^2 + y^2 = 4 \), which subtends a right angle at the origin is

BITSAT - 2026
circle

A passenger sitting in a train A moving at 90 km/h observes another train B moving in the opposite direction for 8 s. If the velocity of the train B is 54 km/h, then length of train B is:

BITSAT - 2026
Relative Velocity

If \( x = \sqrt{2^{\text{cosec}^{-1} t}} \) and \( y = \sqrt{2^{\text{sec}^{-1} t}} (|t| \ge 1) \), then dy/dx is equal to :

BITSAT - 2026
Derivatives of Functions in Parametric Forms

The Bohr orbit radius for the hydrogen atom (n = 1) is approximately 0.530 \AA. The radius for the first excited state (n = 2) orbit is (in \AA)

BITSAT - 2026
Bohr's model of hydrogen atom