Mathematics

# If f(x) is a function satisfying $f\left( \dfrac{1}{x}\right)+x^2f(x)=0$ for all non-zero x, then $\displaystyle \int_{sin\Theta}^{cosec\Theta}f(x)dx$ is equal to

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Subjective Hard Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 105

#### Realted Questions

Q1 Subjective Medium
Solve$\displaystyle \int_0^1 \dfrac{x^2-2}{x^2+1}dx$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
lf $\displaystyle \int\frac{dx}{ae^{mx}+be^{-mx}}=K\tan^{-1} (Pe^{mx} ) +C$, then $K,\ P=$
• A. $K=\displaystyle \frac{1}{\sqrt{ab}},\ P=\sqrt{\frac{a}{b}}$
• B. $\displaystyle K=m\sqrt{ab},P=\sqrt{\frac{b}{a}}$
• C. $K=\displaystyle \frac{1}{m\sqrt{ab}},\ P=\sqrt{\frac{b}{a}}$
• D. $K=\displaystyle \frac{1}{m\sqrt{ab}},\ P=\sqrt{\frac{a}{b}}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Evaluate: $\displaystyle \int _{ 0 }^{ 1 }{ { x\left( 1-x \right) }^{ n } } dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Integrate the function    $x \sin 3x$

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Hard
$\int\, \displaystyle \frac {dx}{sin(x\, -\,a)sin(x\, -\, b)}$
• A. $sec\, (b\, -\, a).\, ln\, \begin{vmatrix}\displaystyle \frac {sin(x\, -\, b)}{sin(x\, -\,a)}\end{vmatrix}\, +\, c$
• B. $sec\, (b\, -\, a).\, ln\, \begin{vmatrix}\displaystyle \frac {sin(x\, +\, b)}{sin(x\, +\,a)}\end{vmatrix}\, +\, c$
• C. $cosec\, (b\, -\, a).\, ln\, \begin{vmatrix}\displaystyle \frac {sin(x\, +\, b)}{sin(x\, +\,a)}\end{vmatrix}\, +\, c$
• D. $cosec\, (b\, -\, a).\, ln\, \begin{vmatrix}\displaystyle \frac {sin(x\, -\, b)}{sin(x\, -\,a)}\end{vmatrix}\, +\, c$