JEE MAIN Definite Integration Previous Year Questions (PYQs) – Page 14 of 17
A Place for Latest Exam wise Questions, Videos, Previous Year Papers,
Study Stuff for MCA Examinations
Study Stuff for MCA Examinations
Let $f(x) = \left| {x - 2} \right|$ and g(x) = f(f(x)), $x \in \left[ {0,4} \right]$. Then
$\int\limits_0^3 {\left( {g(x) - f(x)} \right)} dx$ is equal to:
$\int\limits_0^3 {\left( {g(x) - f(x)} \right)} dx$ is equal to:
1
2
3
4
Solution
The value of the integral $\int\limits_0^{\pi / 4} \frac{x \mathrm{~d} x}{\sin ^4(2 x)+\cos ^4(2 x)}$
1
2
3
4
Solution
For x2 $ \ne $ n$\pi $ + 1, n $ \in $ N (the set of natural numbers), the integral
$\int {x\sqrt {{{2\sin ({x^2} - 1) - \sin 2({x^2} - 1)} \over {2\sin ({x^2} - 1) + \sin 2({x^2} - 1)}}} dx} $ is equal to : (where c is a constant of integration)
$\int {x\sqrt {{{2\sin ({x^2} - 1) - \sin 2({x^2} - 1)} \over {2\sin ({x^2} - 1) + \sin 2({x^2} - 1)}}} dx} $ is equal to : (where c is a constant of integration)
1
2
3
4
Solution
If [x] denotes the greatest integer less than or equal to x, then the value of the integral $\int_{ - \pi /2}^{\pi /2} {[[x] - \sin x]dx} $ is equal to :
1
2
3
4
Solution
The value of $\displaystyle\int_{0}^{\pi}\!\lvert\cos x\rvert^{3}\,dx$ is:
1
2
3
4
Solution
Let the domain of the function $f(x) = \log_2 \log_4 \log_6 (3 + 4x - x^2)$ be $(a, b)$.
If $\int_0^{b - a} [x^2] , dx = p - \sqrt{q - \sqrt{r}}, ; p, q, r \in \mathbb{N}, ; \gcd(p, q, r) = 1$,
where $[,]$ is the greatest integer function, then $p + q + r$ is equal to
1
2
3
4
Solution
If
$2\displaystyle\int_{0}^{1} \tan^{-1} x , dx = \displaystyle\int_{0}^{1} \cot^{-1} (1 - x + x^{2}) , dx,$
then
$\displaystyle\int_{0}^{1} \tan^{-1} (1 - x + x^{2}) , dx$ is equal to :
1
2
3
4
Solution
The function f(x), that satisfies the condition $f(x) = x + \int\limits_0^{\pi /2} {\sin x.\cos y\,f(y)\,dy} $, is :
1
2
3
4
Solution
If $\displaystyle \int_{0}^{\pi/8}\frac{\tan\theta}{\sqrt{2k\,\sec\theta}}\;d\theta
=1-\frac{1}{\sqrt{2}},\ (k>0)$, then the value of $k$ is:
1
2
3
4
Solution
The value of $\displaystyle \int_{0}^{2\pi}\big\lfloor \sin 2x,(1+\cos 3x)\big\rfloor,dx$, where $[\cdot]$ denotes the greatest integer function, is:
1
2
3
4
Solution
JEE MAIN
Online Test Series, Information About Examination,
Syllabus, Notification
and More.
View More
JEE MAIN
Online Test Series, Information About Examination,
Syllabus, Notification
and More.
View More
Ask Your Question or Put Your Review.
