Exams › GATE › Engineering Mathematics

Let f(x) be a continuous function from R to R such that f(x) = 1 − f(2 − x) Which one of the following options is the CORRECT value of ∫₀² f(x) dx ?

1. 0
2. 1
3. 2
4. −1

Correct answer: 1

Solution

The equation f(x) = 1 - f(2 - x) implies that the function has a symmetry around x = 1. When integrating from 0 to 2, the contributions from f(x) and f(2 - x) balance out, leading to the integral equating to 1.

Related GATE Engineering Mathematics questions

• The sum of the following infinite series is: 1/1! + 1/2! + 1/3! + 1/4! + 1/5! +...
• Which one of the following options is the correct Fourier series of the periodic function f(x) described below: f(x) = { 0 if −2 < x < −1 { 2k if −1 < x < 1; period = 4 { 0 if 1 < x < 2
• The value of lim_(x→∞) (x − √(x² + x)) is equal to
• The following inequality is true for all x close to 0. 2 − x²/3 < x sin x/(1 − cos x) < 2 What is the value of lim(x→0) x sin x/(1 − cos x) ?
• A closed thin-walled tube has thickness, t, mean enclosed area within the boundary of the centreline of tube’s thickness, Aₘ, and shear stress, τ. Torsional moment of resistance, T, of the section would be
• Consider the hemi-spherical tank of radius 13 m as shown in the figure (not drawn to scale). What is the volume of water (in m³) when the depth of water at the centre of the tank is 6 m?

⚔️ Practice GATE Engineering Mathematics free + battle 1v1 →