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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]
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these questions are not enough for practice please increase the number of questions
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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 much useful.. Thank you
Monke
Superb
Thanks
superb
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Nice
Questions are good for revision