Q. $\int_{0}^{\pi}[\cot x] d x,$ where $[.]$ denotes the greatest integer function, is equal to –
(1) –1 $
(2)-\frac{\pi}{2}$
(3) $\frac{\pi}{2}$
(4) 1
[AIEEE-2009]
Q. Let p(x) be a function defined on R such that p'(x) = p'(1 – x), for all x $\in$0, 1], p(0) = 1 and p(1) = 41. Then $\int_{0}^{1}$ p(x) dx equals :-
(1) $\sqrt{41}$
(2) 21
(3) 41
(4) 42
[AIEEE-2010]
Q. The value of $\int_{0}^{1} \frac{8 \log (1+x)}{1+x^{2}} d x$ is :-
(1) $\frac{\pi}{2} \log 2$
(2) $\log 2$
(3) $\pi \log 2$
(4) $\frac{\pi}{8} \log 2$
[AIEEE-2011]
Q. Let [.] denote the greatest integet function then the value of $\int_{0}^{1.5} \mathrm{x}\left[\mathrm{x}^{2}\right] \mathrm{dx}$ is :-
( 1)$\frac{5}{4}$ (2) 0 (3) $\frac{3}{2}$ (4) $\frac{3}{4}$
[AIEEE-2011]
Q. If $\mathrm{g}(\mathrm{x})=\int_{0}^{\mathrm{x}} \cos 4 \mathrm{t} \mathrm{dt},$ then $\mathrm{g}(\mathrm{x}+\pi)$ equals :
(1) $\mathrm{g}(\mathrm{X}) \cdot \mathrm{g}(\pi)$
(2) $\frac{\mathrm{g}(\mathrm{x})}{\mathrm{g}(\pi)}$
(3) $\mathrm{g}(\mathrm{x})+\mathrm{g}(\pi)$
(4) $\mathrm{g}(\mathrm{x})-\mathrm{g}(\pi)$
[AIEEE-2012]
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Sol. (3,4)
Q. Statement-I : The value of the integral $\int_{\pi / 6}^{\pi / 3} \frac{\mathrm{dx}}{1+\sqrt{\tan \mathrm{x}}}$ is equal to $\frac{\pi}{6}$
Statement-II : $\int_{a}^{b} f(x) d x-\int_{a}^{b} f(a+b-x) d x$
(1) Statement-I is true, Statement-II is true; Statement-II is a correct explanation for Statement- I.
(2) Statement-I is true, Statement-II is true; Statement-II is not a correct explanation for Statement-I.
(3) Statement-I is true, Statement-II is false.
(4) Statement-I is false, Statement-II is true.
[JEE-MAIN-2013]
Q. The integral $\int_{0}^{\pi} \sqrt{1+4 \sin ^{2} \frac{x}{2}-4 \sin \frac{x}{2}} d x$ equals :
(1) $\pi-4$
(2) $\frac{2 \pi}{3}-4-4 \sqrt{3}$
(3) $4 \sqrt{3}-4$
(4) $4 \sqrt{3}-4-\frac{\pi}{3}$
[JEE-MAIN-2014]
Q. The integral $\int_{2}^{4} \frac{\log x^{2}}{\log x^{2}+\log \left(36-12 x+x^{2}\right)} d x$ is equal to :
(1) 1 (2) 6 (3) 2 (4) 4
[JEE-MAIN-2015]
Q. The integral $\int_{\frac{\pi}{4}}^{\frac{3 \pi}{4}} \frac{\mathrm{dx}}{1+\cos x}$ is equal to :-
(1) –1 (2) –2 (3) 2 (4) 4
[JEE-MAIN-2017]
Q. The value of $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{\sin ^{2} x}{1+2^{x}} d x$ is :
( 1)$\frac{\pi}{2}$
(2) $4 \pi$
(3) $\frac{\pi}{4}$
(4) $\frac{\pi}{8}$
[JEE-MAIN-2018]
these questions are not enough for practice please increase the number of questions
If there will be more questions
Than it will be much better
So increase the number of questions
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Thanks to eSaral
Want more problems
sir can you put some latest years bits
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it is very usefull
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It is very much useful.. Thank you
Monke
Superb
Thanks
superb
An excellent work done by saral…it helped me alot…
Nice
Questions are good for revision