Let $f:[-2, 3] \to [0, \infty)$ be a continuous function such that $f(1-x) = f(x)$ for all $x \in [-2, 3]$. If $R_1$ is the numerical value of the area of the region bounded by $y = f(x)$,$x = -2$,$x = 3$ and the $x$-axis,and $R_2 = \int_{-2}^3 x f(x) dx$,then:
- A$3R_1 = 2R_2$
- B$2R_1 = 3R_2$
- C$R_1 = R_2$
- D$R_1 = 2R_2$
Explore More
Similar Questions
If $(a, b)$ is the orthocentre of the triangle whose vertices are $(1, 2), (2, 3)$ and $(3, 1)$,and $I_1 = \int_{a}^{b} x \sin(4x - x^2) dx$,$I_2 = \int_{a}^{b} \sin(4x - x^2) dx$,then $36 \frac{I_1}{I_2}$ is equal to:
DifficultJEE MAIN 2024
View SolutionThe value of $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{1}{[x]+4} dx$, where $[\bullet]$ denotes the greatest integer function, is
DifficultJEE MAIN 2026
View SolutionIf $M = \int_{0}^{\pi / 2} \frac{\cos x}{x+2} dx$ and $N = \int_{0}^{\frac{\pi}{4}} \frac{\sin x \cos x}{(x+1)^{2}} dx$, then the value of $M-N$ is
MediumWBJEE 2018
View SolutionIf $f(a+b-x)=f(x)$,then $\int_a^b x f(x) d x=$ . . . . . . .
The value of $\int_{4}^{7} \frac{(11-x)^{2}}{x^{2}+(11-x)^{2}} d x$ is
Vedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo