Mathematics

# The value of the defined integral $\displaystyle \int^{\pi/2}_{0}(\sin x+\cos x)\sqrt {\dfrac {e^{x}}{\sin x}}dx$ equals

$2\sqrt {e^{\pi/2}}$

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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 Hard
Evaluate the given integral.
$\displaystyle\int { \cfrac { \cos { 2x } -\cos { 2\theta } }{ \cos { x } -\cos { \theta } } } dx$
• A. $2\left( \sin { x } -x\cos { \theta } \right) +C$
• B. $2\left( \sin { x } +2x\cos { \theta } \right) +C\quad$
• C. $2\left( \sin { x } -2x\cos { \theta } \right) +C$
• D. $2\left( \sin { x } +x\cos { \theta } \right) +C$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
Match the following.
I.$\displaystyle \int e^{x}(\sin x+\cos x)dx=$               a)$e^{x}\tan x+c$
II.$\ \displaystyle \int e^{x}(\cos x-\sin x)dx=$            b)$e^{x}\log\sec x+c$
III.$\ \displaystyle \int e^{x}(\tan x+\sec^{2}x)dx=$        c)$e^{x}\sin x+c$
IV. $\displaystyle \int e^{x} (\tan x+ \log \sec x)dx=$     d)$e^{x}\cos x+c$
• A. I-a, II- b, III- c, IV- d
• B. I-b, II- c, III- a, IV- d
• C. I-b, II- d, III- c, IV- a
• D. I-c, II- d, III- a, IV- b

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Evaluate the following integral as the limit of sum:
$\displaystyle\int^2_0x^3dx$.

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate the following integral:
$\displaystyle\int^{\pi}_0\dfrac{dx}{(6-\cos x)}$.

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
$\int { (\cfrac { { 2 }^{ x }-5^{ x } }{ 10^{ x } } )dx }$ is equal to __________________.
• A. $\cfrac { { 2 }^{ x } }{ \log _{ e }{ 2 } } -\cfrac { 5^{ x } }{ \log _{ e }{ 5 } } +c$
• B. $\cfrac { { 2 }^{ x } }{ \log _{ e }{ 2 } } +\cfrac { 5^{ x } }{ \log _{ e }{ 5 } } +c$
• C. $\cfrac { { 5 }^{ -x } }{ \log _{ e }{ 5 } } -\cfrac { 2^{ -x } }{ \log _{ e }{ 2 } } +c$
• D. $\cfrac { { 2 }^{ -x } }{ \log _{ e }{ 2 } } -\cfrac { 5^{ -x } }{ \log _{ e }{ 5 } } +c$