Mathematics

# The value of the definite integral $\int^{3\pi/4}_0[(1+x)sin x + (1-x) cosx] dx$ is

$2 tan\dfrac{3\pi}{8}$

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

#### Realted Questions

Q1 Subjective Hard
Evaluate the given integral.
$\displaystyle \int { \cfrac { { x}^{ 2 }-1 }{ { x }^{ 4 }+{ x }^{ 2 }+1 } } dx$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\displaystyle \int \frac{\sec x}{\log \left ( \sec x+\tan x \right )}dx$
• A. $\displaystyle \log \left [ \log \left ( \sec x-\tan x \right ) \right ].$
• B. $\displaystyle \log \left [ \log \left ( \sin x+\cos x \right ) \right ].$
• C. $\displaystyle \log \left [ \log \left ( \sin x-\cos x \right ) \right ].$
• D. $\displaystyle \log \left [ \log \left ( \sec x+\tan x \right ) \right ].$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
$\displaystyle \int x\sin x\sec ^{3}x dx$ is equal to
• A. $\displaystyle \frac{1}{2}\left [ \sec^{2}x-\tan x \right ]+c$
• B. $\displaystyle \frac{1}{2}\left [ x\sec^{2}x+\tan x \right ]+c$
• C. $\displaystyle \frac{1}{2}\left [\sec^{2}x+\tan x \right ]+c$
• D. $\displaystyle \frac{1}{2}\left [ x\sec^{2}x-\tan x \right ]+c$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Integrate $\displaystyle \int { \dfrac { { \sec }^{ 2 }x }{ \tan x } } dx$

$\displaystyle\int e^x\left(\dfrac{1}{x}-\dfrac{1}{x^2}\right)\ dx$.