Mathematics

# Let $\displaystyle\int _{ 0 }^{ 1 }{ \dfrac { { e }^{ t }dt }{ 1+t } }$ then $\displaystyle \int _{ a-1 }^{ a }{ \dfrac { { e }^{ t }dt }{ t-a-1 } }$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 109

#### Realted Questions

Q1 Single Correct Hard
If $f(x) = x - x^2 +1$ & $g(x)=max\left \{ f(t) ;0\leq t< x \right \}$, then $\overset {1}{\underset { 0 }{ \int } } g (x) dx = ?$
• A. $\dfrac{7}{6}$
• B. $\dfrac{5}{4}$
• C. none of these
• D. $\dfrac{29}{24}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Evaluate the following definite integral:
$\displaystyle \int_{1}^{2}\dfrac {1}{\sqrt {(x-1) (2-x)}}dx$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
If $y(x-y)^{2}=x$ then $\displaystyle\int { \cfrac { 1 }{ x-3y } dx }$ is
• A. $\dfrac{1}{4}\ln { \left( { \left( x-y \right) }^{ 2 }-1 \right) }$
• B. $\dfrac{1}{2}\ln { \left( { \left( x-y \right) }^{ 2 }-1 \right) }$
• C. $\dfrac{1}{6}\left( \ln { \left( { x }^{ 2 }-{ y }^{ 2 } \right) } -1 \right)$
• D. $\dfrac{1}{3}\ln { \left( 1+{ \left( x-y \right) }^{ 2 } \right) }$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
$\displaystyle{\int e^{x} \left \{\dfrac {1 + \sin x \cos x}{\cos^{2}x}\right \}dx =}$
• A. $e^{x}\cos x + c$
• B. $e^{x} \sec x \tan x + c$
• C. $e^{x} \cos^{2}x - 1 + c$
• D. $e^{x} \tan x + c$

Prove that $\displaystyle\int_0^{\pi/2}$ $ln(\sin x)dx=\displaystyle\int_0^{\pi/2}ln(cos x)dx=\int_0^{\pi/2}\,\,ln(sin2x)dx=-\dfrac{\pi}{2}.ln 2$.