Mathematics

# Let  $\theta$  be the angle between the lines  ${ L }_{ { 1 } }:\left[ \begin{array}{l} { { x }=2{ t }+{ 1 } } \\ { { y }={ t }+{ 1 } } \\ { { z }=3{ t }+{ 1 } } \end{array} \right.$  and  ${ L }_{ { 2 } }:\left[ \begin{array}{l} { { x }=3{ s }+2 } \\ { { y }=6{ s }-1 } \\ { { z }=4 } \end{array} \right.$  where  $s , t \in { R }.$  Then the value of  $\int _ { 0 } ^ { \theta } \dfrac { 1 } { 1 + \tan x } d x =$

$\pi / 6$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

#### Realted Questions

Q1 Single Correct Medium
Evaluate $\displaystyle \int xsecx.tanxdx=$
• A. $x\sec x+\log|\tan(\pi/2+x/2)|+c$
• B. $x\sec x-\log |\tan(\pi/4+x)|+c$
• C. $x\sec x+\log|\tan x/2|+c$
• D. $x\sec x-\log$$|\tan(\pi/4+x/2)|+c$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Solve :
$I = \int \dfrac {e^x}{ e^{2x} - 3e^x + 1 } dx$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
The value of $\displaystyle \int \tan^{2}\ xdx$ equals
• A. $\tan x-x+c$
• B. $\cot x+x+c$
• C. $-\tan x-x+c$
• D. $\tan x+x+c$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate : $\int {{2^{{2^{{2^x}}}}}{2^{{2^x}}}{2^x}dx.}$

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