Consider the integrals I_ 1 = _ 0 ^ 1 e^ -x ^ 2 x d x, I_ 2 = _ 0 ^ 1 e^ -x^ 2 ^ 2 x d x…
Mathematics · JEE Advanced · NTA Exams — Integral Calculus
Consider the integrals
\(I_{1}=\int_{0}^{1} e^{-x} \cos ^{2} x d x, I_{2}=\int_{0}^{1} e^{-x^{2}} \cos ^{2} x d x\)
\(I_{3}=\int_{0}^{1} e^{-\frac{x^{2}}{2}} \cos ^{2} x d x, I_{4}=\int_{0}^{1} e^{-\frac{x^{2}}{2}} d x\) Then
\(I_{1}=\int_{0}^{1} e^{-x} \cos ^{2} x d x, I_{2}=\int_{0}^{1} e^{-x^{2}} \cos ^{2} x d x\)
\(I_{3}=\int_{0}^{1} e^{-\frac{x^{2}}{2}} \cos ^{2} x d x, I_{4}=\int_{0}^{1} e^{-\frac{x^{2}}{2}} d x\) Then
- \(\mathrm{I}_{2}>\mathrm{I}_{4}>\mathrm{I}_{1}>\mathrm{I}_{3}\)
- \(\mathrm{I}_{2}<\mathrm{I}_{4}<\mathrm{I}_{1}<\mathrm{I}_{3}\)
- \(\mathrm{I}_{1}<\mathrm{I}_{2}<\mathrm{I}_{3}<\mathrm{I}_{4}\)
- \(\mathrm{I}_{1}>\mathrm{I}_{2}>\mathrm{I}_{3}>\mathrm{I}_{4}\)
Answer
(C) I _ 1
Sign up free on Edukali to view the step-by-step worked solution and practice thousands of similar questions.
Related practice questions
- If the integrand is a rational function of x and fractional powers of a linear fractional function of the…
- The area of the closed figure bounded by the curves y= x , y= 4-3 x y=0 is
- If _ 0 ^ x f(t) d t=x+ _ x ^ 1 t f(t) d t then f(1) is
- We can derive reduction formula for the integration of the form ^ n x d x, ^ n x d x, ^ n x d x and other…
- Area of the region bounded by y e^ x and y x , is
- If I= d x (a^ 2 -b^ 2 x^ 2 )^ 3 / 2
- Let f : [–1, 2] → [0, ∞ ) be a continuous function such that f ( x ) = f (1 – x ) for all x ∈ [–1, 2]. Let R_…
- Using integral _ 0 ^ / 2 ( x) d x =- _ 0 ^ / 2 ( x) d x=- 2 2 _ 0 ^ / 2 ( x) d x=0 and _ 0 ^ / 4 (1+ x) d x=…
More Integral Calculus questions · Browse all practice questions