New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Definite Integration question

2021 · 18 Mar · Shift 2 · Q30

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Definite Integration
2021 · 18 Mar · Shift 2 · Q30

Definite Integration question

2021 · 18 Mar · Shift 2 · Q30

JEE MainMathematicsDefinite IntegrationMCQ+4 / −1

Let g(x) =

\int_0^x {f(t)dt}

, where f is continuous function in [ 0, 3 ] such that

{1 \over 3} \le

f(t)

\le

1 for all t

\in

[0, 1] and 0

\le

f(t)

\le {1 \over 2}

for all t

\in

(1, 3]. The largest possible interval in which g(3) lies is :

A
$\left[ { - 1, - {1 \over 2}} \right]$
B
$\left[ { - {3 \over 2}, - 1} \right]$
C
[1, 3]
D
$\left[ {{1 \over 3},2} \right]$

More from Definite Integration

Let P(x) be a real polynomial of degree 3 which vanishes at x = $-$ 3. Let P(x) have local minima at x = 1, local maxima at x = $-$ 1 and $- 1 \int 1 P (x) d x$ = 18, then the sum of all the coefficients of the polynomial P(x) is…2021 · Numerical
Let a be a positive real number such that $\int_{0}^{a} e^{x - [x]} d x = 10 e - 9$ where [ x ] is the greatest integer less than or equal to x. Then a is equal to:2021 · MCQ
The value of the integral $- 1 \int 1 lo g_{e} (1 - x + 1 + x) d x$ is equal to:2021 · MCQ
If [x] denotes the greatest integer less than or equal to x, then the value of the integral $\int_{- π /2}^{π /2} [[x] - sin x] d x$ is equal to :2021 · MCQ
If the real part of the complex number $(1 - cos θ + 2 i sin θ)^{- 1}$ is $\frac{1}{5}$ for $θ \in (0, π)$ , then the value of the integral $\int_{0}^{θ} sin x d x$ is equal to:2021 · MCQ
Let $g (t) = \int_{- π /2}^{π /2} cos (\frac{π}{4} t + f (x)) d x$ , where $f (x) = lo g_{e} (x + x^{2} + 1), x \in R$ . Then which one of the following is correct?2021 · MCQ
If $0 \int 100 π \frac{s i n ^{2} x}{e ^{(\frac{x}{π} - [\frac{x}{π}])}} d x = \frac{α π ^{3}}{1 + 4 π ^{2}}, α \in R$ where [x] is the greatest integer less than or…2021 · MCQ
$x \to 0 lim \frac{0 \int x ^{2} ( s i n t ) d t}{x ^{3}}$ is equal to :2021 · MCQ