Mathematics

# Integrate:$\int _{ -\pi }^{ \pi }{ \dfrac { 2x(1+\sin { x } ) }{ 1+{ cos }^{ 2 }x } } { dx }\\$ is?

$\\ \dfrac { { \pi }^{ 2 } }{ 4 }$

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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
If $f(x) \begin{vmatrix} x & cosx & e^{ { x^{ 2 } } } \\ sin\quad x & x^{ 2 } & sec\quad x \\ tan\quad x & x^ 4 & 2x^ 2 \end{vmatrix}$ then $\displaystyle \int_{-\pi/2}^{\pi/2}f(x)dx=$
• A. $1$
• B. $2$
• C. $3$
• D. $0$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
If $\displaystyle f\left ( x \right )$ and $\displaystyle g\left ( x \right )$ be continuous functions over the closed interval $\displaystyle \left [ 0, a \right ]$ such that $\displaystyle f\left ( x \right )= f\left ( a-x \right )$ and $\displaystyle g\left ( x \right )+g\left ( a-x \right )= 2.$ Then $\displaystyle \int_{0}^{a}f\left (x \right )\dot g\left (x \right )dx$ is equal to
• A. $\displaystyle \int_{0}^{a}g\left ( x \right )dx$
• B. $\displaystyle 2a$
• C. none of these
• D. $\displaystyle \int_{0}^{a}f\left ( x \right )dx$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Find: $\displaystyle\int { \dfrac { { \left( { x }^{ 4 }-x \right) }^{ \dfrac { 1 }{ 4 } } }{ { x }^{ 5 } } } dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
$\int { { cosec }^{ 3 }x } dx$

The value  of the definite integral, $I = \int _{ 0 }^{ \sqrt { 10 } }{ \dfrac { x }{ { e }^{ { x }^{ 2 } } } } dx$ is equal to