If $I$ is the greatest of the definite integrals
${I_1} = \int_0^1 {{e^{ - x}}{{\cos }^2}x\,dx} , \,\, {I_2} = \int_0^1 {{e^{ - {x^2}}}} {\cos ^2}x\,dx$
${I_3} = \int_0^1 {{e^{ - {x^2}}}dx} ,\,\,{I_4} = \int_0^1 {{e^{ - {x^2}/2}}dx} ,$ then
${I_1} = \int_0^1 {{e^{ - x}}{{\cos }^2}x\,dx} , \,\, {I_2} = \int_0^1 {{e^{ - {x^2}}}} {\cos ^2}x\,dx$
${I_3} = \int_0^1 {{e^{ - {x^2}}}dx} ,\,\,{I_4} = \int_0^1 {{e^{ - {x^2}/2}}dx} ,$ then
- A$I = {I_1}$
- B$I = {I_2}$
- C$I = {I_3}$
- D$I = {I_4}$
Explore More
Similar Questions
If $[ \cdot ]$ represents the greatest integer function,then $\int_{-1}^1 (x[1+\sin(\pi x)]+1) dx = $
By using the properties of definite integrals,evaluate the integral $\int_{0}^{\frac{\pi}{2}}(2 \log \sin x-\log \sin 2 x) d x$.
Difficult
View SolutionFor any integer $n$, the value of the integral $\int_0^\pi e^{\cos^2 x} \cos^3(2n+1)x \, dx$ is:
MediumWBJEE 2024
View SolutionThe value of $\int_{-2}^{2} \left[ p \ln \left( \frac{1+x}{1-x} \right) + q \ln \left( \frac{1-x}{1+x} \right)^{-2} + r \right] dx$ depends on:
Difficult
View SolutionThe value of $\int_{0}^{1} \frac{dx}{x + \sqrt{1 - x^2}}$ is
Medium
View SolutionVedclass 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