Mathematics

# If $\int _{ 0 }^{ 100 }{ f\left( x \right) dx=a }$, then $\sum _{ r=1 }^{ 100 }{ \int _{ 0 }^{ 1 }{ (f\left( r-1+x \right) dx) } }$=

$a$

Its FREE, you're just one step away

Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 114

#### Realted Questions

Q1 One Word Hard
The value of $\displaystyle \frac{\left ( \sqrt{2}+1 \right )198}{\pi }\int_{\pi /4}^{3\pi /4}\displaystyle \frac{\phi }{1 + \sin \phi }\:d\phi$ is

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Evaluate the given integral.
$\displaystyle \int { \cfrac { { x }^{ 2 } }{ 1+{ x }^{ 3 } } } dx$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Integrate:
$\displaystyle\int{x\sqrt{{{x}^{2}}+2}}dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Hard
$\displaystyle \int(\frac{\cos^{3}x+\cos^{5}x}{\sin^{2}x+\sin^{4}x})dx=$
• A. $\sin x +\displaystyle \frac{2}{\sin x}-6 \tan^{-1}(\sin x)+c$
• B. $\sin x -\displaystyle \frac{2}{\sin x}+6 \tan^{-1} (\sin x)+c$
• C. $\sin x+\dfrac{2}{\sin x}+6 \tan^{-1}(\sin x)+c$
• D. $\sin x -\displaystyle \frac{2}{\sin x}-6\tan^{-1}(\sin x)+c$

1 Verified Answer | Published on 17th 09, 2020

Q5 Passage Hard
Given that for each $\displaystyle a \in (0, 1), \lim_{h \rightarrow 0^+} \int_h^{1-h} t^{-a} (1 -t)^{a-1}dt$ exists. Let this limit be $g(a)$
In addition, it is given that the function $g(a)$ is differentiable on $(0, 1)$