Mathematics

# $\displaystyle \int _{ 0 }^{ 2010 }{(x-[x]) }dx$ is equal to

$1005$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

#### Realted Questions

Q1 Single Correct Medium
$\displaystyle \int\frac{d{x}}{\cos x-\sin x}=$
• A. $\displaystyle \frac{1}{\sqrt{2}}\log|\tan(\frac{x}{2}-\frac{\pi}{8})|+c$
• B. $\displaystyle \frac{1}{\sqrt{2}}\log|\tan(\frac{x}{2}+\frac{3\pi}{8})|+c$
• C. $\displaystyle \frac{1}{\sqrt{2}}\log|\cot(\frac{x}{2})|+c$
• D. $\displaystyle \frac{1}{\sqrt{2}}\log|\tan(\frac{x}{2}-\frac{3\pi}{8})|+c$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Hard
Evaluate the following integrals:-
$\int {\dfrac{{x + 1}}{{\sqrt {{x^2} - x + 1} }}dx}$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Hard
Prove that : $\displaystyle \int_{0}^{1} \tan^{-1} x dx = \dfrac {\pi}{4} - \dfrac {1}{2}\log 2$.

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Integrate the function    $f'(ax+b)[f(ax+b)]^n$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q5 Passage Medium
Let $\displaystyle f\left ( x \right )=\frac{\sin 2x \cdot \sin \left ( \dfrac{\pi }{2}\cos x \right )}{2x-\pi }$

Then answer the following question.

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020