Project ForgeEngineering Mathematics
Calculus
GATE 2011
Easy
If f(x) is an even function and a is a positive real number, then the definite integral of f(x) from -a to a equals
- A0
- Ba
- C2a
- 2 × (integral of f(x) from 0 to a)
Explanation
For an even function (f(-x)=f(x)), the contributions from [-a,0] and [0,a] are identical, so ∫[-a,a] f(x)dx = 2∫[0,a] f(x)dx.
Source: GATE ME 2011 (2011)
This question is part of a 15-day revision cycle — sign in and Project Forge will bring it back the day before you'd forget it.